Factor Investigation
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The document defines and provides examples of prime, composite, factors, proper factors, perfect, deficient, and abundant numbers. Prime numbers have exactly two factors, one and itself. Composite numbers have more than two factors. Perfect numbers have a sum of proper factors equal to the target number, like 6. Deficient numbers have a sum of proper factors less than the target number, like 8. Abundant numbers have a sum of proper factors greater than the target number, like 12.
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Prime numbers,whole numbers and composite numbers
Prime numbers,whole numbers and composite numbersQUAID E AWAM UNIVERSITY OF ENGINEERING SCIENCE AND TECHONOLOGY NAWABSHAH
Prime numbers are numbers that have only 2 factors: 1 and themselves. For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. By contrast, numbers with more than 2 factors are call composite numbers.Primecomposite
1) A prime number is a number that has exactly two factors: itself and 1. For example, 7 is prime because the only numbers that divide into it are 1 and 7.
2) A composite number has more than two factors. For example, 8 has four factors: 1, 2, 4, and 8.
3) One is neither a prime nor composite number. It only has one factor, which is itself.
Prime Numbers
This document discusses prime numbers, composite numbers, and how to determine which category a whole number falls into. It provides that:
- Prime numbers have exactly two unique factors - the number itself and 1.
- Composite numbers have more than two factors.
- Only the numbers 0, 1, and 2 are neither prime nor composite - 0 because every number divides it, and 1 because it only has one factor. All other whole numbers are either prime or composite.
Prime Number
A prime number is a whole number greater than 1 that is only divisible by 1 and itself. A composite number is one that has divisors other than 1 and itself. The document then explains that prime numbers follow a pattern of being multiples of 6 plus or minus 1 (6n±1), and provides a two-step process for determining if a number is prime or composite: 1) check if it is a multiple of 6 plus or minus 1, and 2) check if it is divisible by any numbers up to its square root.
Number systems
This document provides an overview of different number systems:
1. It defines six types of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
2. Natural numbers are used for counting and start at 1. Whole numbers are natural numbers with 0 included. Integers include whole numbers and their negatives.
3. Rational numbers can be written as fractions with integer numerators and denominators. Irrational numbers cannot be written as fractions with integers and have non-repeating decimals.
4. Real numbers include all rational and irrational numbers.
Perfect numbers
This document defines a perfect number as a number where the sum of all its factors (excluding the number itself) equals the number. It provides 6 and 28 as examples of perfect numbers. It then explains a method for finding perfect numbers by taking the product of (2p-1) and 2p-1, where p is a prime number, and lists the first 3 perfect numbers found using this method: 6, 28, and 496. It challenges the reader to find the next perfect number and first 10 perfect numbers using this method.
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The document discusses prime and composite numbers. Prime numbers are integers that are only divisible by 1 and themselves, with examples including 7, 11, and 13. Composite numbers have more than two factors, like 8 which is divisible by 1, 2, 4, and 8. The document provides examples of prime and composite numbers and notes that these categories only apply to positive integers, not negative numbers.
Numeral System
A numeral is a sign, or figure that represents a number. It is a mathematical numbering system. In other words, A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols.
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2) A composite number has more than two factors. For example, 8 has four factors: 1, 2, 4, and 8.
3) One is neither a prime nor composite number. It only has one factor, which is itself.
Prime Numbers
This document discusses prime numbers, composite numbers, and how to determine which category a whole number falls into. It provides that:
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- Composite numbers have more than two factors.
- Only the numbers 0, 1, and 2 are neither prime nor composite - 0 because every number divides it, and 1 because it only has one factor. All other whole numbers are either prime or composite.
Prime Number
A prime number is a whole number greater than 1 that is only divisible by 1 and itself. A composite number is one that has divisors other than 1 and itself. The document then explains that prime numbers follow a pattern of being multiples of 6 plus or minus 1 (6n±1), and provides a two-step process for determining if a number is prime or composite: 1) check if it is a multiple of 6 plus or minus 1, and 2) check if it is divisible by any numbers up to its square root.
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This document provides an overview of different number systems:
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2. Natural numbers are used for counting and start at 1. Whole numbers are natural numbers with 0 included. Integers include whole numbers and their negatives.
3. Rational numbers can be written as fractions with integer numerators and denominators. Irrational numbers cannot be written as fractions with integers and have non-repeating decimals.
4. Real numbers include all rational and irrational numbers.
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This document defines a perfect number as a number where the sum of all its factors (excluding the number itself) equals the number. It provides 6 and 28 as examples of perfect numbers. It then explains a method for finding perfect numbers by taking the product of (2p-1) and 2p-1, where p is a prime number, and lists the first 3 perfect numbers found using this method: 6, 28, and 496. It challenges the reader to find the next perfect number and first 10 perfect numbers using this method.
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A numeral is a sign, or figure that represents a number. It is a mathematical numbering system. In other words, A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols.
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Factor Investigation
- 2. Natural or Counting Numbers Can you remember the difference between prime and composite? Prime numbers have exactly 2 factors, (one and itself). Composite numbers have more than two factors.
- 3. Factors The numbers that when multiplied together make the original number or target. The factors of 10 are 1, 2, 5, and 10
- 4. Proper Factors To find the proper factors, you use every factor except the target number Example: remember the factors of 10 are 1, 2, 5, and 10 The Proper Factors are only 1, 2, and 5 (we do not get to use 10 because it is the “target”)
- 5. Perfect Numbers This happens when the sum of the proper factors is equal to the target number Example: 6 . Its factors are 1, 2, 3, 6 The proper factors are 1, 2, and 3. Add the proper factors together and you get 6, which is the target number. That makes it perfect.
- 6. Deficient Numbers To be a deficient number, the sum of its proper factors is less than the target. Example: 8 The factors are 1, 2, 4 and 8 The proper factors are 1, 2, and 4 Added together, the proper factors equal 7 and that is less than 8 so it is deficient.
- 7. Abundant Numbers To be an abundant number, the sum of the proper factors is greater than the target. Example: 12: factors are 1, 2, 3, 4, 6, 12 Proper factors are 1, 2, 3, 4, 6 Add the proper factors and get 16 which is bigger than the target number 12. That makes it abundant.