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  1. A list of divisibility rules for 2, 3, 4, 5, 6, 7, 8, 9, 10 with examples. Divisibility Rules. We say that a number is divisible if it can be divided evenly with no.
  2. A divisibility rule is a shorthand way of discovering whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix, and they are all different, we present rules only for decimal numbers. 1 Divisibility rules for numbers 120 2 Step-by-step examples 2.1 Divisibility by 2 2.2.
  3. For explanation of general divisibility rules explained, see Divisibility Rules. For Mobile Devices, it is strongly recommended to view this page in 'PC mode', or simply view the Divisibility Rules page above. Below is a List of Divisibility Rules sorted by number. 1 Difficulty Coding 2 Divisibility of Numbers below 5 3 Divisibility of Numbers between 6 and 10 4 Divisibility of Numbers between.
  4. Why Does the Divisibility Rule for 3 Work? The divisibility rule for 3 works because the number represented by each digit can be written as a multiple of 9 plus that digit. 9 is divisible by 3 so if the sum of the digits is divisible by 3, the number itself is too. Here is the proof that 3174 is divisible by 3.
is a algorithm of determining whether a given number is divisible by a fixed divisor without performing the division.

Divisibility by 2

The number is divided by 2 when the last digit is even (0, 2, 4, 6, or 8).

Divisibility by 12: The number should be divisible by both 3 3 3 and 4 4 4. Divisibility by 13: The sum of four times the units digits with the number formed by the rest of the digits must be divisible by 13 13 1 3 (this process can be repeated for many times until we arrive at a sufficiently small number).

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 3

The number is divided by 3 when the sum of the digits is divided by 3.

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=313).

Divisibility by 4

The number is divided by 4 when the number formed by the last two digits is divisible by 4.

The two-digit number is divisible by 4 when twice the tens digit, plus the ones digit is divisible by 4.

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=212).

Divisibility by 5

The number is divided by 5 when the last digit is 0 or 5.

375, 5680, 233575 — divided by 5, as the last digit of this numbers is 0 or 5;

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9634, 452, 389753 — not divided by 5, as the last digit of this numbers isn't 0 or 5.

Divisibility by 6

The number is divided by 6 when it divided by 2 and 3.

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);

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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=623);

34681 — not divided by 6, as it divided by 2 (last digits of the number isn't even).

Divisibility by 9

The number is divided by 9 when the sum of the digits is divided by 9.

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=249).

Divisibility

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Divisibility by 10

The number is divided by 10 when the last digit is 0.

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.

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Divisibility by 11

The number is divided by 11 if the sum of digits standing in even places is equal to the sum of digits standing in odd places or divided by 11.

242 — is divided by 11, as the sum of the numbers in odd positions S2n+1 = 2 + 2 = 4; sum of digits in even positions S2n = 4 and S2n+1 = S2n.

319 — is divided by 11, as the sum of the numbers in odd positions S2n+1 = 3 + 9 = 12; sum of digits in even positions S2n = 1, and their difference S2n+1 - S2n = 11 - divided by 11.

919380 — is divided by 11, as the sum of the numbers in odd positions S2n+1 = 9 + 9 + 8 = 26; sum of digits in even positions S2n = 1 + 3 + 0 = 4, and their difference S2n+1 - S2n = 22 - divided by 11.

2838 — is divided by 11, as the sum of the numbers in odd positions S2n+1 = 2 + 3 = 5; sum of digits in even positions S2n = 8+ 8 = 16, and their difference S2n - S2n+1 = 11 - divided by 11.

244 — is not divided by 11, as the sum of the numbers in odd positions S2n+1 = 2 + 4 = 6; sum of digits in even positions S2n = 4 and their difference S2n+1 - S2n = 2 - not divided by 11.

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