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Divisibility Rules Dividing by 2 1. All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8. Dividing by 3 1. Add up all the digits in the number. 2. Find out what the sum is. If the sum is divisible by 3, so is the number Dividing by 4 1. Are the last two digits in your number divisible by 4? 2. If so, the number is too! 3. For example: 358912 ends in 12 which is divisible by 4, thus so is 358912. Dividing by 5 1. Numbers ending in a 5 or a 0 are always divisible by 5. Dividing by 6 1. If the Number is divisible by 2 and 3 it is divisible by 6 also. Dividing by 7 (2 Tests) Take the last digit in a number. Double and subtract the last digit in your number from the rest of the digits. Repeat the process Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7. Dividing by 8 1. This one's not as easy, if the last 3 digits are divisible by 8, so is the entire number. 2. Example: 6008 - The last 3 digits are divisible by 8, therefore, so is 6008. Dividing by 9 1. Almost the same rule and dividing by 3. Add up all the digits in the number. 2. Find out what the sum is. If the sum is divisible by 9, so is the number. 3. For example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too! Dividing by 10 1. If the number ends in a 0, it is divisible by 10. Divisibility Rules Worksheet www.edonyourown.com Divisibility Rules By Janine Bouyssounouse The divisibility rules make math easier. Did you ever wonder how people could tell if something was divisible by a number just by looking at it? These rules are how they do it. Memorize a few simple rules and simplifying fractions and prime factorization will be so much easier. Number Divisibility Rule Example Two (2) A number is divisible by two if it is even. Another way to say a word is even is to say it ends in 0, 2, 4, 6 or 8. 642 is divisible by two because it ends in a two, which makes it an even number Three (3) A number is divisible by three if the sum of the digits adds up to a multiple of three. 423 is divisible by three because 4 + 2 + 3 = 9. Since nine is a multiple of three (or is divisible by three), then 423 is divisible by three Four (4) A number is divisible by four if it is even and can be divided by two twice. 128 is divisible by four because half of it is 64 and 64 is still divisible by two Five (5) A number is divisible by five if it ends in a five or a zero. 435 is divisible by five because it ends in a five Six (6) A number is divisible by six if it is divisible by both two and three. 222 is divisible by six because it is even, so it is divisible by two and its digits add up to six, which makes it divisible by three Nine (9) A number is divisible by nine if the sum of the digits adds up to a multiple of nine. This rule is similar to the divisibility rule for three. 9243 is divisible by nine because the sum of the digits adds up to eighteen, which is a multiple of nine Ten (10) A number is divisible by ten if it ends in a zero. This rule is similar to the divisibility rule for five. 730 is divisible by ten because it ends in zero Divisibility Rules Worksheet www.edonyourown.com Divisibility Rules Practice Problems Use the divisibility rules to circle the answers. Number Divisible By: Example: 10 2 3 4 5 6 9 10 15 27 36 16 28 57 102 268 4518 93 144 256 75 450 70 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10