What are the Divisibility rules of 14 15 18?

Answer 1

14...

Checking for divisibility by 14 would combine the rules for 2 and 7, since 2x7 = 14

The rule for 2 is that the last digit of the number is even (0,2,4,6 or 8).

There is no real rule for 7, but there is one way of testing divisibility by 7 that I have come up with, although rather complicated. First, write your number, then beneath it, under each digit from right to left, write out the numbers 1,3,2,6,4,5 in that order and keep repeating the sequence until each digit of your number has another digit beneath it. Use only the amount of digits needed. Then, multiply each digit of your number by the digit beneath it, and add all of these new numbers. If the number you get is a multiple of 7, the number you began with was also a multiple of 7.

Example for 7:

We are checking 3192847 for divisibility by 7...

3 1 9 2 8 4 7

1 5 4 6 2 31

1x3 + 5x1 + 4x9 + 6x2 + 2x8 + 3x4 + 1x7

= 3 + 5 + 36 + 12 + 16 + 12 + 7

91

We can test 91 again to find divisibility...

9 1

3 1

3x9 + 1x1 = 28

28 is a multiple of 7 (it is 4 x 7), so 91 and 3192847 must also be multiples of 7. 3192847 is actually 456121 x 7.

If both of these tests work, the number must be a multiple of 14.

15...

Divisibility by 15 can be tested by combining the rules for 3 and 5.

The rule for 3 is that the sum of all the digits in the number is a multiple of 3.

The rule for 5 is that the number ends in 5 or 0.

If both of these tests work, the number must be a multiple of 15.

18...

Checking for divisibility by 18 combines the divisibility rules for 2 and 9.

Once again, a number is divisible by 2 if its last digit is even.

A number is divisible by 9 if the sum of its digits is a multiple of 9.

If both of these tests work, the number must be divisible by 18.