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Divisibility Tests Mr. Burres [7th Grade Math]

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Divisibility Tests We use divisibility tests to quick determine if a value is a factor of another value. Though we can always divide to determine if a value is a factor of another value, the tests can often take less time.

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Divisibility Tests Divisibility Test Divisibility Test 2 A number is divisible by 2 (has a factor of 2) if… the number is even If a number is even (ends in 0, 2, 4, 6, or 8), then the number is divisible by 2. Examples: 18 is divisible by 2, because it is even (it ends in 8) 123 is not divisible by 2, it is not even (it ends in 3)

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Divisibility Tests Divisibility Test Divisibility Test 3 A number is divisible by 3 (has a factor of 3) if… the sum of its digits is divisible by 3 If you add all the digits of a number, and the sum is divisible by 3, then so is the original number. Examples: 114 is divisible by 3, because 1+1+4 = 6, and 6 is divisible by 3 223 is not divisible by 3, because 2+2+3 = 7, and 7 is not divisible by 3

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Divisibility Tests Divisibility Test Divisibility Test 4 A number is divisible by 4 (has a factor of 4) if… the last two digits, as a single value, is divisible by 4 If you can divide the last two digits of a number (as a single value) by 4, then the entire number is divisible by 4. Examples: 312 is divisible by 4, because 12 is divisible by 4. 526 is not divisible by 4, because 26 is not divisible by 4.

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Divisibility Tests Divisibility Test Divisibility Test 5 A number is divisible by 5 (has a factor of 5) if… the number ends in 5 or 0 If a number ends in 5 or 0, then it is divisible by 5. Examples: 7,955 is divisible by 5, because it ends in 5. 5,551 is not divisible by 5, because it ends in 1, not 5 or 0.

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Divisibility Tests Divisibility Test Divisibility Test 6 A number is divisible by 6 (has a factor of 6) if… the number is divisible by both 2 AND 3 If a number is divisible by both 2 and 3, then it is also divisible by 6. Examples: 132 is divisible by 6, because 132 is divisible by 2 and 3. 164 is not divisible by 6, because, although it IS divisible by 2, it is NOT divisible by 3.

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Divisibility Tests Divisibility Test Divisibility Test 7 A number is divisible by 7 (has a factor of 7) if… its divisible by 7 Though there are divisibility tests for 7, it is quicker to just divide. Examples: 714 is divisible by 7, 714 divided by 7 is 102, remainder 0. 421 is not divisible by 7, 421 divided by 7 is 60, remainder 1.

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Divisibility Tests Divisibility Test Divisibility Test 8 A number is divisible by 8 (has a factor of 8) if… the last three digits, as a single value, is divisible by 8 If you can divide the last three digits of a number (as a single value) by 8, then the entire number is divisible by 8. Examples: 3,816 is divisible by 8, because 816 is divisible by 8. 14,167 is not divisible by 8, because 167 is not divisible by 8.

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Divisibility Tests Divisibility Test Divisibility Test 9 A number is divisible by 9 (has a factor of 9) if… the sum of its digits is divisible by 9 If you add all the digits of a number, and the sum is divisible by 9, then so is the original number. Examples: 954 is divisible by 9, because 9+5+4 = 18, and 18 is divisible by 9 983 is not divisible by 9, because 9+8+3 = 20, and 20 is not divisible by 9

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Divisibility Tests Divisibility Test Divisibility Test 10 A number is divisible by 10 (has a factor of 10) if… the number ends in 0 If a number ends in 0, then it is divisible by 10. Examples: 7,950 is divisible by 10, because it ends in 0. 541 is not divisible by 10, because it ends in 1, not 0.

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Divisibility Tests Divisibility Test Divisibility Test 11 A number is divisible by 11 (has a factor of 11) if… its divisible by 11 Though there are divisibility tests for 11, it is quicker to just divide. Examples: 374 is divisible by 11, because 374 divided by 11 is 34, remainder 0. 461 is not divisible by 11, because 461 divided by 11 is 41, remainder 10.

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Divisibility Tests Divisibility Test Divisibility Test 12 A number is divisible by 12 (has a factor of 12) if… the number is divisible by both 3 AND 4 If a number is divisible by both 3 and 4, then it is also divisible by 12. Examples: 132 is divisible by 12, because 132 is divisible by 3 and 4. 164 is not divisible by 12, because, although it IS divisible by 4, it is NOT divisible by 3.

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Divisibility Tests Divisibility Test Divisibility Test 13 A number is divisible by 13 (has a factor of 13) if… its divisible by 13 Though there are divisibility tests for 13, it is quicker to just divide. Examples: 286 is divisible by 13, because 286 divided by 13 is 22, remainder 0. 573 is not divisible by 13, because 573 divided by 13 is 44, remainder 1.

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Divisibility Tests Divisibility Test Divisibility Test 14 A number is divisible by 14 (has a factor of 14) if… the number is divisible by both 2 AND 7 If a number is divisible by both 2 and 7, then it is also divisible by 14. Examples: 154 is divisible by 14, because 154 is divisible by 2 and 7. 217 is not divisible by 14, because, although it IS divisible by 7, it is NOT divisible by 2.

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Divisibility Tests Divisibility Test Divisibility Test 15 A number is divisible by 15 (has a factor of 15) if… the number is divisible by both 3 AND 5 If a number is divisible by both 3 and 5, then it is also divisible by 15. Examples: 135 is divisible by 15, because 135 is divisible by 3 and 5. 205 is not divisible by 15, because, although it IS divisible by 5, it is NOT divisible by 3.

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