Is 382169 is it divisible by 8 and explain why?

Answer 1

No.

All multiples of 8 are even (end in 2, 4, 6, 8 or 0) but 382169 is odd (ends in 1, 3, 5, 7 or 9) so it cannot be a multiple of 8 and thus cannot be divisible by 8.

To test for any [even] number being divisible by 8 add the units digit to twice the tens digit to four times the hundreds digit; if this sum is divisible by 8, then so is the original number. If the test is repeated until a single digit remains, only if this digit is 8 is the original number divisible by 8, otherwise if it is 1-7 it gives the remainder when the original number is divided by 8 (if it is 9, the remainder is 1).

For 382169 this gives 9 + 2x6 + 4x1 = 9 + 12 + 4 = 25. 25 is not divisible by 8, so 382169 is not divisible by 8.

Using the test on 25 gives 5 + 2x2 + 4x0 = 9, again not divisible by 8 (remainder is 1).