Divisibility of 7623

Answer 1

7623 is divisible by 3.

Test of divisibility by 3:

Sum of digits of 7623 = 7+6+2+3 = 18, which is a multiple of 3, so the number is divisible by 3.

If sum of the digits of a number is a multiple of 9 then it is divisible by 9.

So, 7623 is also divisible by 9.

Therefore, test of divisibility can help a lot in determining whether a number is divisible by any other number.

Answer 2

A number is a multiple of 7623 if it's a multiple of 7, 9 and 121 at the same time

7623 = 3^2 x 7 x 11^2 = 9 x 7 x 121

A number is a multiple of 7 if the difference between twice the last digit and the rest of the number is a multiple of 7

A number is a multiple of 9 if the sum of the digits is a multiple of 9

A number is a multiple of 121 if the difference between 12 times the last digit and the rest of the number is a multiple of 121

For example 15246 is a multiple of 7 because 1524 - 6 x 2 = 1512 and 1512 is a multiple of 7. It's a multiple of 9 because 1 + 5 + 2 + 4 + 6 = 18 and 18 is a multiple of 9. It's a multiple of 121 because 1524 - 6 x 12 = 1452 and 1452 is a multiple of 121. Since it's a multiple of 7, 9 and 121 it means it's a multiple of 7623