# Is 896 divisible by 2 3 5 9 or 10?

896 is only divisible by 2; it is not divisible by 3, 5, 9 nor 10.

To be divisible by 2, the number must be even, ie, the last digit must be even, that is one of {0, 2, 4, 6, 8}; 896 ends in 6 which is even, thus 896 is divisible by 2.

To be divisible by 3, add the digits of the number together and if the sum is divisible by 3, then so is the original number. The test can be repeated on the sum until a single digit remains; if this single digit is 3, 6, or 9 then the original number is divisible by 3: 896 → 8 + 9 + 6 = 23 → 2 + 3 = 5 which is not one of {3, 6, 9}, thus 896 is not divisible by 3

To be divisible by 5, the last digit must be 0 or 5; 896 ends in 6 which is neither 0 nor 5, so 896 is not divisible by 5.

To be divisible by 9, add the digits of the number together and if the sum is divisible by 9, then so is the original number. The test can be repeated on the sum until a single digit remains (which is called the digital root of the number); only if this single digit is 9 will the original number be divisible by 9: 896 → 8 + 9 + 6 = 23 → 2 + 3 = 5 which is not one 9 thus 896 is not divisible by 9;

To be divisible by 10 the last digit must be 0; 896 ends if 6 which is not 0, so 896 is not divisible by 10.

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