What is the divisibility rule for 65?

Answer 1

For a number to be divisible by 65 it must be divisible by 5 and by 13.

To be divisible by 5 it must end in 5 or 0.

Checking for divisibility by 13 is a bit harder:

• split the number into two parts: X = the number formed by all but the last digit and U = the last digit.
• test X + 4U for divisibility by 13.
• if necessary split the answer in two again and test.
• if you don't know your 13 times table well then keep going until the answer is 13, 26 or 39 (once you get there then X + 4U will simply repeat).

For example, to check 1767675 for divisibility by 65.

The number ends in 5 so it is divisible by 5 and it remains to be seen if it is divisible by 13.

X = 176767 and U = 5 so X + 4U = 176787: a number that is too big so have another go.

X = 17678 and U = 7 so X + 4U = 17706: still too big, so another go.

X = 1770 and U = 6 so X + 4U = 1794: still too big, so another go.

X = 179 and U = 4 so X + 4U = 195: not really too big but you could have another go

X = 19 and U = 5 so X + 4U = 39 Bingo!

if you repeat,

X = 3, U = 9 and X + 4U = 39.

So the number is divisible by 13.

Divisibility by 5 and 13 implies divisibility by 65.

Answer 2

65 is divisible by:

1 because everything is.

5 because it ends in 5.