Which numbers are divisible by 4?

Answer 1

Multiplying 4 by any other integer (whole number) gives you a multiple of 4. By this definition, all multiples of 4 are divisible by 4, as dividing a whole number times 4 by 4 will give you a whole number.

Any whole number with:

• A 4 or 8 in the units position and an even number in the tens position (eg. 4, 8, 24, 44)
• A 2 or 6 in the units position and an odd number in the tens position (eg. 12, 16, 32, 56)

is a multiple of 4 (because 20≡0 (mod 4), and 10≡2 (mod 4)).

The hundreds, thousands and all other columns are not relevant, because

10n = 2n x 5n

∀n>2, n∈ℤ , 2n=22x2k, where 22,2k∈ℤ

Hence, 10n=4 x 25 x 10k, which means that all multiples of powers of 10 greater than 100 are divisible by 4.