Is 745 divisible by 2 3 5 9 or 10?

Answer 1

Out of that list, just 5.

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To be divisible by 2 the last digit must be even, ie one of {0, 2, 4, 6, 8}

The last digit is 5 which is not even (it is odd), so 745 is not divisible by 2

To be divisible by 3 the sum of the digits must also be divisible by 3; if the summing is repeated until a single digit remains, then the original number is only divisible by 3 if this single digit is divisible by 3, ie it is one of {3, 6, 9}

745 → 7 + 4 + 5 = 16

16 + 1 + 6 = 7

7 is not divisible by 3 (it is not one of {3, 6, 9}), so 745 is not divisible by 3

To be divisible by 5, the last digit must be 0 or 5

The last digit of 745 is 5 which is one of {0, 5}, so 745 is divisible by 5

To be divisible by 9 the sum of the digits must also be divisible by 9; if the summing is repeated until a single digit remains, then the original number is only divisible by 9 if this single digit is 9 (otherwise this single digit gives the remainder when the original number is divided by 9)

745 + 7 + 4 + 5 = 16

16 → 1 + 6 = 7

7 is not 9, so 745 is not divisible by 9 (the remainder is 7)

To be divisible by 10 the last digit must be 0

The last digit of 745 is 5 which is not 0, so 745 is not divisible by 10.

745 is not divisible by 2, 3, 9, 10

745 is divisible by 5.