Divisibility Rules for 7

A number is divisible by 7 if unit’s place digit is multiplied by 2 and subtracted from the remaining digits and the number obtained is divisible by 7.
Example of Divisibility Rules for 7,

1680 7 = 1680 – 7 × 2 = 1666
It is difficult to decide whether 1666 is divisible by 7 or not. In such cases, we continue the process again and again till it becomes easy to decide whether the number is divisible by 7 or not.
166 6 → 166 – 6 x 2 = 154
Again 15 4 → 15 – 4 x 2 = 7, divisible by 7
Hence 16807 is divisible by 7.

There two rules which can be used to test divisibility by 7:

Rule 1:

In this divisibility Rule for 7, take away the last digit, double it, subtract it from the truncated original number and continue doing this till only one digit remains. If this is often zero or seven, then the original number is divisible by seven. For example, to check divisibility of 12264 by 7, we do the following calculations:
1226 – 8 = 1218
121 – 16 = 105
10 – 10 = 0
Thus, 12264 is divisible by 7.

Rule 2:

In this divisibility Rule for 7, We first Arrange the digits of the number in reverse order, that is, from right to left, multiplying them successively by the digits 1, 3, 2, 6, 4, 5, repetition with this sequence of multipliers as long as necessary. Then add the product. If the resulting total is divisible by seven, then the original number is divisible by seven. for example, to check divisibility of 12264 by seven, we simply check
4(1) + 6(3) + 2(2) + 2(6) + 1(4) = 4 + 18 + 4 + 12 + 4 = 42, a two-digit number divisible by 7.

Hence, 12264 must also be divisible by 7.

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