Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- Module 2 lesson 19 by mlabuski 352 views
- the division algorithm by Jeneva Clark 1589 views
- Euclid's division algorithm by Shubham Kumar 69 views
- Remainder theorem by Department of Edu... 2217 views
- Number Theory in Discrete Mathematics by Adil Aslam 624 views
- Is unit 4_number_theory by Sarthak Patel 811 views

No Downloads

Total views

1,819

On SlideShare

0

From Embeds

0

Number of Embeds

5

Shares

0

Downloads

46

Comments

0

Likes

1

No embeds

No notes for slide

- 1. The Division Algorithm<br />
- 2. Before we study divisibility, we must remember the division algorithm.<br />r<br />dividend = (divisor ⋅ quotient) + remainder<br />
- 3. A number is divisible by another number if the remainder is 0 and quotient is a natural number.<br />Divisibility <br />
- 4. If a number is divided by itself then quotient is 1.<br />If a number is divided by 1 then quotient is itself.<br />If 0 is divided by any none zero number then quotient is 0.<br />If any number is divided by zero then quotient is undefined.<br />Some remarks:<br />
- 5. Divisibility by 2:<br /> A natural number is divisible by 2 if it is even, i.e. if its units (last) digit is 0, 2, 4, 6, or 8.<br />Divisibility Rules<br />Example: Check if each number is divisible by 2.<br />a. 108 b. 466 c. 87 682 d. 68 241<br />e. 76 543 010<br />
- 6. Divisibility by 3:<br /> A natural number is divisible by 3 if the sum of the digits in the number is multiple of 3.<br />Divisibility Rules<br />Example: Determine whether the following numbers are divisible by 3 or not.<br /> 7605<br /> 42 145<br />c) 555 555 555 555 555<br />
- 7. Divisibility by 4:<br /> A natural number is divisible by 4 if the last two digits of the number are 00 or a multiple of 4.<br />Divisibility Rules<br />Example: Determine whether the following numbers are divisible by 4 or not.<br /> 7600<br /> 47 116<br />c) 985674362549093<br />
- 8. Divisibility Rules<br />Example: 5m3 is a three-digit number where m is a digit. If 5m3 is divisible by 3, find all the possible values of m.<br />Example: a381b is a five-digit number where a and b are digits. If a381b is divisible by 3, find the possible values of a + b.<br />
- 9. Divisibility Rules<br />Example: t is a digit. Find all the possible values of t if:<br />a) 187t6 is divisible by 4.<br />b) 2741t is divisible by 4.<br />
- 10. Divisibility Rules<br />Divisibility by 5:<br />A natural number is divisible by 5 if its last digit is 0 or 5.<br />Example: m235m is a five-digit number where m is a digit. If m235m is divisible by 5, find all the possible values of m.<br />
- 11. Divisibility Rules<br />Divisibility by 6:<br />A natural number is divisible by 6 if it is divisible by both 2 and 3.<br />Example: Determine whether the following numbers are divisible by 6 or not.<br /> 4608<br /> 6 9030<br />c) 22222222222<br />
- 12. Divisibility Rules<br />Example: 235mn is a five-digit number where m and n are digits. If 235mn is divisible by 5 and 6, find all the possible pairs of m, n.<br />
- 13. Divisibility Rules<br />Divisibility by 8:<br />A natural number is divisible by 8 if the number formed by last three digits is divisible by 8.<br />Example: Determine whether the following number is divisible by 8 or not.<br />5 793 128<br />7265384<br />456556<br />
- 14. Divisibility Rules<br />Divisibility by 9:<br />A natural number is divisible by 9 if the sum of the digits of the number is divisible by 9.<br />Example: 365m72 is a six-digit number where m is a digit. If 365m72 is divisible by 9, find all the possible values of m.<br />Example: 5m432n is a six-digit number where m and n are digits. If 5m432n is divisible by 9, find all the possible values of m + n.<br />
- 15. Divisibility Rules<br />Divisibility by 10:<br />A natural number is divisible by 10 if its units (last) digit is 0.<br />Example: is 3700 divisible by 10?<br />
- 16. Divisibility Rules<br />Divisibility by 11:<br />A natural number is divisible by 11 if the difference between the sum of the odd-numbered digits and the sum of the even-numbered digits is a multiple of 11.<br />Example: is 5 764 359 106 divisible by 11?<br />

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment