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“Guzinta”

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1. “Guzinta” By Troy Pomeroy Horace Mann Middle School

2. Why use Divisibility Rules? • Ever wonder if 3 “guzinta” (goes into) numbers like 75235? • How would you find out? • Would you have to divide 75235 by 3? • Would a calculator help? • What if you wanted to check to see if 7 “guzinta” 75235? • Would this process take a long time?

3. Want to learn a FASTER way? I Knew you would!!!!!

4. Testing For Divisibility • Lucky for us, mathematicians older than Mr. Evans developed some rules to determine if certain numbers “guzinta” other numbers without having to divide! • By learning these rules you will be able to perform math tasks like factoring, simplifying fractions, dividing, and problem solving much easier.

5. READY? Here come the “tricks of the trade” known as . . . Divisibility Rules

6. Divisibility Rules • A number is divisible by 2 if it is EVEN. • That means the last digit of the number is 2, 4, 6, 8, or 0. • For example: 35,718 IS divisible by 2 because its last digit is 8 - an even number. 35,719IS NOT divisible by 2 because its last digit is 9 - an odd number.

7. Divisibility Rules • If the sum of the digits is divisible by three, the number is also. • For example, 717 IS divisible by 3 because 7 + 1 + 7 = 15. 15 is divisible by 3 so 717 is divisible by 3 also. • 713 IS NOT divisible by 3 since 7 + 1 + 3 = 11 and 11 is not divisible by 3.

8. Divisibility Rules • The test to see if a number is divisible by 4 is to look at the last two digits of the number. • If those two digits are divisible by 4, then the number is also. • EXAMPLE: 15,912IS divisible by 4 because 12 is divisible by 4. 15,914IS NOT divisible by 4 because 14 is not divisible by 4.

9. Divisibility Rules • If the last digit of a number is 5 or 0, the number is divisible by 5. • EXAMPLE: 366,789,475IS divisible by 5 since it ends in a 5. 366,789,472IS NOT divisible by 5 since it ends in a 2.

10. Divisibility Rules • For a number to be divisible by 6, it must be divisible by BOTH 2 AND 3. • That means it must be EVEN and its digits must add up to a multiple of 3. • EXAMPLE: 315 IS NOT divisible by 6, even though its digits add up to 9, because it is not even. 216 IS divisible by 6 since it is even AND its digits sum to a multiple of 3.

11. Divisibility Rules • If the sum of the digits is divisible by nine, the number is also. • For example, 558 IS divisible by 9 because 5 + 5 + 8 = 18. 18 is divisible by 9 so 558 is divisible by 9 also. • 713 IS NOT divisible by 9 since 7 + 1 + 3 = 11 and 11 is not divisible by 9.

12. Divisibility Rules • A number is divisible by 10 if it ends in 0. • EXAMPLE: 671,320 IS divisible by 10 because it ends in 0. 671,325 IS NOT divisible by 10 since it DOES NOT end in 0.