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**Objective: Learn to test for divisibility.**

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Divisibility: One whole number is divisible by another if, after dividing, the remainder is zero. For example: 18 is divisible by 9 since 18 ÷ 9 = 2 with no remainder. If one whole number is divisible by another number, then the second number is a factor of the first number. For example: Since 18 is divisible by 9, 9 is a factor of 18.

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**A divisibility test is a rule for determining whether one whole number is divisible by another.**

There is a quick way to find factors of large numbers Divisibility rules: A number is divisible by 2… if the last digit is 0, 2, 4, 6 or 8. A number is divisible by 3… if the sum of the digits is divisible by 3. A number is divisible by 4… if the number formed by the last 2 digits is divisible by 4. A number is divisible by 5… if the ones digit is 0 or 5. A number is divisible by 6… if the number is divisible by BOTH 2 and 3 A number is divisible by 8… if the number formed by the last 3 digits is divisible by 8. A number is divisible by 9… if the sum of the digits is divisible by 9. A number is divisible by 10… if the ones digit is 0.

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**For example: Test the number 4,320 for divisibility by 2,3,4,5,6,8,9, and 10.**

Is this number divisible by… 2? Yes, because the last digit is 0. 3? Yes, because = 9 and 9 is divisible by 3. 4? Yes, because the number formed by the last 2 digits (20) is divisible by 4. 5? Yes, because 4,320 ends in 0. 6? Yes, because 4320, is divisible by BOTH 2 and 3. 8? Yes, because the number formed by the last 3 digits (320) is divisible by 8. 9? Yes, because = 9 , which is divisible by 9. 10? Yes, because the ones digit is 0. So, 4,320 is divisible by 2, 3, 4, 5, 6, 8, 9, and 10.

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Your Example: Test each number for divisibility by 2,3,4,5,6,8,9 and 10.

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**Homework: Test the following numbers for divisibility by 2,3,4,5,6,8,9, and 10.**

582 585 330 45 276

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