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## “Guzinta”

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**“Guzinta”**By Troy Pomeroy Horace Mann Middle School**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?**Want to learn a FASTER way?**I Knew you would!!!!!**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.**READY?**Here come the “tricks of the trade” known as . . . Divisibility Rules**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.**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.**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.**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.**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.**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.**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.