Divisibility Tests Mr. Burres [7th Grade Math]

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.

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)

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 = 6, and 6 is divisible by is not divisible by 3, because = 7, and 7 is not divisible by 3

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 is not divisible by 4, because 26 is not divisible by 4.

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.

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 is not divisible by 6, because, although it IS divisible by 2, it is NOT divisible by 3.

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 is not divisible by 7, 421 divided by 7 is 60, remainder 1.

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.

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 = 18, and 18 is divisible by is not divisible by 9, because = 20, and 20 is not divisible by 9

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 is not divisible by 10, because it ends in 1, not 0.

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 is not divisible by 11, because 461 divided by 11 is 41, remainder 10.

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 is not divisible by 12, because, although it IS divisible by 4, it is NOT divisible by 3.

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 is not divisible by 13, because 573 divided by 13 is 44, remainder 1.

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 is not divisible by 14, because, although it IS divisible by 7, it is NOT divisible by 2.

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 is not divisible by 15, because, although it IS divisible by 5, it is NOT divisible by 3.