
Divisibility rulesA divisibility rule is a algorithm of determining whether a given number is divisible by a fixed divisor without performing the division.
Divisibility by 2
Divisibility by 3
Divisibility by 4
Divisibility by 5
Divisibility by 6
Divisibility by 9
Divisibility by 10
Divisibility tests
Divisibility by 2The number is divided by 2 when the last digit is even (0, 2, 4, 6, or 8). Examples:
2, 8, 16, 24, 66, 150 — divided by 2, as the last digits of the numbers is even; 3, 7, 19, 35, 77, 453 — not divided by 2, as the last digit of the number is odd. Divisibility by 3The number is divided by 3 when the sum of the digits is divided by 3. Examples:
75 — divided by 3, as 7+5=12, and the number 12 is divided by 3 (12:3=4); 471 — divided by 3, as 4+7+1=12, and the number 12 is divided by 3 (12:3=4); 532 — not divided by 3, as 5+3+2=10, and the number 10 is not divided by 3 (10:3=3 Divisibility by 4The number is divided by 4 when the number formed by the last two digits is divisible by 4. The twodigit number is divisible by 4 when twice the tens digit, plus the ones digit is divisible by 4. Examples:
4576 — divided by 4, as last two digits 76 divided by 4 (7·2+6=20, 20:4=5); 9634 — not divided by 4, as last two digits 34 not divided by 4 (3·2+4=10, 10:4=2 Divisibility by 5The number is divided by 5 when the last digit is 0 or 5. Examples:
375, 5680, 233575 — divided by 5, as the last digit of this numbers is 0 or 5; 9634, 452, 389753 — not divided by 5, as the last digit of this numbers isn't 0 or 5. Divisibility by 6The number is divided by 6 when it divided by 2 and 3. Examples:
462 — divided by 6, as it divided by 2 (last digits of the number is even) and divided by 3 (sum of the digits is divided by 3: 4+6+2=12, 12:3=4); 3456 — divided by 6, as it divided by 2 (last digits of the number is even) and divided by 3 (sum of the digits is divided by 3: 3+4+5+6=18, 18:3=6); 24642 — divided by 6, as it divided by 2 (last digits of the number is even) and divided by 3 (sum of the digits is divided by 3: 2+4+6+4+2=18, 18:3=6); 861 — not divided by 6, as it not divided by 2 (last digits of the number isn't even); 3458 — not divided by 6, as it divided by 3 (sum of the digits is not divided by 3: 3+4+5+8=20, 20:3=6 34681 — not divided by 6, as it divided by 2 (last digits of the number isn't even). Divisibility by 9The number is divided by 9 when the sum of the digits is divided by 9. Examples:
69759 — divided by 9, as sum of the digits is divided by 9 (6+9+7+5+9=36, 36:9=4); 34681 — not divided by 9, as sum of the digits is not divided by 9 (3+4+6+8+1=22, 22:9=2 Divisibility by 10The number is divided by 10 when the last digit is 0. Examples:
460, 24000, 1245464570 — divided by 10, as the last digit of this numbers is 0; 234, 25048, 1230000003 — не делятся на 10, as the last digit of this numbers isn't 0. Add the comment 