Divisibility
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The document outlines various rules for determining if a number is divisible by 2, 3, 4, 5, 6, 9, or 10. For each rule, it provides examples of numbers that satisfy or do not satisfy the rule's divisibility test. The rules are: a number is divisible by 2 if its last digit is even; divisible by 3 if the sum of its digits is a multiple of 3; divisible by 4 if the last two digits are a multiple of 4 or are 00; divisible by 5 if it ends in 5 or 0; divisible by 6 if it is divisible by both 2 and 3; divisible by 9 if the sum of its digits is a multiple of 9; and divisible by 10 if it ends in
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Division, divisibility rules 11 3-10
This document outlines divisibility rules to determine factors of numbers based on their digits. The rules are: if the ones digit is even, the number is divisible by 2; if the sum of the digits is divisible by 3, the number is divisible by 3; if the number ends in 0 or 5, it is divisible by 5; if the sum of the digits is divisible by 9, the number is divisible by 9; and if a number ends in 0, it is divisible by 10. Examples are provided for each rule.
Divisability rules
The document discusses divisibility rules for numbers 2 through 10. It provides examples for each rule and interactive exercises for the reader to determine which numbers are and are not divisible by certain criteria. The main rules covered are:
- A number is divisible by 2 if the last digit is even
- A number is divisible by 3 if the sum of its digits is divisible by 3
- A number is divisible by 4 if the last two digits are divisible by 4
- A number is divisible by 5 if the last digit is 0 or 5
- A number is divisible by 6 if it is divisible by both 2 and 3
- A number is divisible by 9 if the sum of its digits is divisible by 9
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Divisability Rules
This document provides explanations and examples of divisibility rules for numbers 2 through 12. It explains what it means for a number to be divisible by another number without a remainder. It then gives the specific rules for divisibility by numbers 2 through 12, such as a number being divisible by 2 if the last digit is even. Examples are provided for each rule along with practice problems for the user to determine which numbers are or are not divisible based on the rules.
Divisibility Rules
This document discusses divisibility rules to determine if a number is divisible by certain factors. It provides the following rules:
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- A number is divisible by 2 if it ends in an even digit.
- A number is divisible by 4 if the last two digits are divisible by 4.
- A number is divisible by 5 if it ends in 5 or 0.
- A number is divisible by 8 if the last three digits are divisible by 8.
- A number is divisible by 6 if it is divisible by both 2 and 3.
Divisibility rules
This document discusses divisibility rules, which are ways to determine if one number can be divided evenly by another number without a remainder. It provides the rules for divisibility by 2, 3, 4, 5, 6, 8, 9, 10 and notes there is no simple rule for 7. The rules are based on patterns in the digits of the number being divided. For example, a number is divisible by 2 if the last digit is even, and divisible by 3 if the sum of the digits is 3, 6, or 9. The document also provides examples and asks the reader to apply the rules to several numbers.
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The document provides information about divisibility rules for numbers 2 through 10. It explains what it means for a number to be divisible by another number without a remainder. It then gives the divisibility rules for numbers 2 through 10, providing examples for each. It tests the reader with practice problems asking them to identify which number is not divisible by the given number. The document encourages the reader to practice more if needed and provides positive feedback.
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This document provides divisibility rules for numbers 1 through 20. It lists the tests used to determine if a number is divisible by each number from 1 to 20. For each rule, it provides an example number and step-by-step working to show the rule being applied. The rules involve examining digits of the number, performing operations on the digits like addition and subtraction, and checking if the resulting values are divisible by the given number.
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This document describes tests that can be used to determine if a number is divisible by other numbers from 2 to 12. For each number, it provides the rule to check divisibility and examples of applying the rule. The tests check the ones/last digits, sum of digits, or applying multiple tests in sequence like being divisible by both 2 and 3 for divisibility by 6. These simple tests can help determine divisibility without fully dividing the numbers.
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This document outlines divisibility rules to determine factors of numbers based on their digits. The rules are: if the ones digit is even, the number is divisible by 2; if the sum of the digits is divisible by 3, the number is divisible by 3; if the number ends in 0 or 5, it is divisible by 5; if the sum of the digits is divisible by 9, the number is divisible by 9; and if a number ends in 0, it is divisible by 10. Examples are provided for each rule.
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The document discusses divisibility rules for numbers 2 through 10. It provides examples for each rule and interactive exercises for the reader to determine which numbers are and are not divisible by certain criteria. The main rules covered are:
- A number is divisible by 2 if the last digit is even
- A number is divisible by 3 if the sum of its digits is divisible by 3
- A number is divisible by 4 if the last two digits are divisible by 4
- A number is divisible by 5 if the last digit is 0 or 5
- A number is divisible by 6 if it is divisible by both 2 and 3
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This document provides explanations and examples of divisibility rules for numbers 2 through 12. It explains what it means for a number to be divisible by another number without a remainder. It then gives the specific rules for divisibility by numbers 2 through 12, such as a number being divisible by 2 if the last digit is even. Examples are provided for each rule along with practice problems for the user to determine which numbers are or are not divisible based on the rules.
Divisibility Rules
This document discusses divisibility rules to determine if a number is divisible by certain factors. It provides the following rules:
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- A number is divisible by 2 if it ends in an even digit.
- A number is divisible by 4 if the last two digits are divisible by 4.
- A number is divisible by 5 if it ends in 5 or 0.
- A number is divisible by 8 if the last three digits are divisible by 8.
- A number is divisible by 6 if it is divisible by both 2 and 3.
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This document discusses divisibility rules, which are ways to determine if one number can be divided evenly by another number without a remainder. It provides the rules for divisibility by 2, 3, 4, 5, 6, 8, 9, 10 and notes there is no simple rule for 7. The rules are based on patterns in the digits of the number being divided. For example, a number is divisible by 2 if the last digit is even, and divisible by 3 if the sum of the digits is 3, 6, or 9. The document also provides examples and asks the reader to apply the rules to several numbers.
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This document describes tests that can be used to determine if a number is divisible by other numbers from 2 to 12. For each number, it provides the rule to check divisibility and examples of applying the rule. The tests check the ones/last digits, sum of digits, or applying multiple tests in sequence like being divisible by both 2 and 3 for divisibility by 6. These simple tests can help determine divisibility without fully dividing the numbers.
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One Stop Learning Station developed with an objective of connecting the dots to ascertain knowledge that could lead you to a differentiating source of competitive advantage in today's world after going through the expansive information sources e.g. CBSE study Material, various Books, Guides, Notes, and assignments to answer your queries.
So if you are a Knowledge seeking person then follow and subscribe us
Twitter: https://twitter.com/EschoolMaths
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> A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits.
1> Any Integer is divisible by 1
2> The last digit of the number is even or 0
3> The sum of the digits is divisible by 3
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9> The sum of the digits is divisible by 9
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The document discusses various concepts related to numbers including positive integers, prime numbers, composite numbers, and divisibility tests. It provides definitions and examples of prime numbers, composite numbers, and tests for divisibility by numbers from 2 to 18. The divisibility tests covered include divisibility by sums of digits, last digits, and performing operations on digits. Examples are provided to demonstrate the divisibility tests.
Divisibility
The document discusses divisibility rules and concepts related to prime and composite numbers. It provides definitions and examples of divisors, divisibility rules, prime numbers, composite numbers, prime factorization, greatest common divisor (GCD), and lowest common multiple (LCM). Divisibility rules allow testing if one number can be evenly divided by another without calculation. Prime numbers have only two factors, one and itself, while composite numbers have more than two factors. Prime factorization involves writing a composite number as a product of prime factors. The GCD is the largest number that divides into a group of numbers, and the LCM is the lowest number that all numbers in a group divide into evenly.
Lesson 9 divisibility rules
This document discusses divisibility rules, which are shorthand techniques for determining if a number is divisible by another number without performing long division. It provides the divisibility rules for numbers 1 through 13. The rules for numbers like 2, 5, and 10 simply involve checking the last digit(s) of the number. Rules for other numbers like 3, 4, 9 involve adding or subtracting digits. The rules for 7 and 11 are more complex and involve repeatedly doubling, subtracting, and checking remainders. Examples are provided to demonstrate each rule.
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The document discusses various properties of squares and square roots. It defines a square number as the result of multiplying a number by itself. Some key points made include:
- Numbers ending in 2, 3, 7, or 8 cannot be perfect squares, while numbers ending in 1, 4, 5, 6, or 9 may be squares
- The units digit of a square number depends on the units digit of the original number
- Odd squares are odd numbers and even squares are even numbers
- A number is not a perfect square if it ends in an odd number of zeros
- The Pythagorean theorem relates the squares of the sides of a right triangle
- Square roots can be estimated and found using repeated subtraction
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Divisibility
- 2. Rule: If it ends with a 0, 2, 4, 6, or 8 Number Divisible? Why? 456 Yes The last digit is 6 68 Yes The last digit is 8 25 No The last digit is 5 (not a 2,4,6,or 8) 207 No The last digit is 7 (not a 2,4,6,or 8) Divisible by 2?
- 3. Rule: If the sum of the digits is a multiple of 3 Number Divisible? Why? 405 Yes 4 + 0 + 5 = 9 (9 is a multiple of 3) 381 Yes 3 + 8 + 1 = 12 (12 is a multiple of 3) 928 No 9 + 2 + 8 = 19 (19 is not a multiple of 3) 4,616 No 4 + 6 + 1 + 6 = 17 (17 is not a multiple of 3) Divisible by 3?
- 4. Rule: If the last two digits are a multiple of 4 (or if the last two digits are 00) Number Divisible? Why? 348 Yes 48 is a multiple of 4 27,616 Yes 16 is a multiple of 4 8,514 No 14 is not a multiple of 4 722 No 22 is not a multiple of 4 1,200 Yes The last two digits are 00 200 is a multiple of 4 Divisible by 4?
- 5. Rule: If it ends with a 5 or a 0 Number Divisible? Why? 3,425 Yes The last digit is 5 750 Yes The last digit is 0 8,551 No The last digit is 1 (not a 0 or a 5) 394 No The last digit is 4 (not a 0 or a 5) Divisible by 5?
- 6. Rule: If it is divisible by 2 and by 3 Number Divisible? Why? 5,106 Yes The last digit is a 2 (it is a multiple of 2 ) and... 5 + 1 + 0 + 6 = 12 (12 is a multiple of 3) 636 Yes The last digit is a 6 (it is a multiple of 2 ) and... 6 + 3 + 6 = 15 (15 is a multiple of 3) 5,912 No The last digit is a 2 (it is a multiple of 2 ) but... 5 + 9 + 1 + 2 = 17 (17 is not a multiple of 3) 508 No The last digit is a 8 (it is a multiple of 2 ) but... 5 + 0 + 8 = 13 (13 is not a multiple of 3) Divisible by 6?
- 7. Rule: If the sum of the digits are a multiple of 9 Number Divisible? Why? 7,686 Yes 7 + 6 + 8 + 6 = 27 (27 is a multiple of 9) 252 Yes 2 + 5 + 2 = 9 (9 is a multiple of 9) 883 No 8 + 8 + 3 = 19 (19 is not a multiple of 9) 5,105 No 5 + 1 + 0 + 5 = 11 (11 is not a multiple of 9) Divisible by 9?
- 8. Rule: If the last digit is 0 Number Divisible? Why? 880 Yes The last digit is 0 9,560 Yes The last digit is 0 312 No The last digit is 2 (not a 0) 7,897 No The last digit is 7 (not a 0) Divisible by 10?