Divisibility rules single digit

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How can we determine if a large integer is evenly divisible by a certain number?

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For dividing by 1, any integer is divisible by 1

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Even numbers can all be divided by 2, so look for final digits of 0, 2, 4, 6, or 8

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If we add up the digits, and that sum is divisible by 3, then we know the number is divisible by 3. For example, 165 has a sum of its digits of 1 plus 6 plus 5, which is 12. 12 is divisible by 3, so we know that 165 is divisible by 3

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To see if a number is divisible by 4, we only need to look at the last 2 digits, because any multiple of 100 is divisible by 4. in 1752, we can look at 52 and see that it is divisible by 4, so we know 1752 must be.

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Any number that ends in either a 5 or a 0 is divisible by 5

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To be divisible by 6 a number must be divisible by 3 and by 2, so we follow both of those rules.

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To see if a number is divisible by 8, we only need to look at the last 3 digits, because any multiple of 1000 is divisible by 8. in 7120, we can look at 120 and see that it is divisible by 8, so we know 7120 must be.

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If we add up the digits, and that sum is divisible by 9, then we know the number is divisible by 9. For example, 4248 has a sum of its digits of 4 plus 2 plus 4 plus 8, which is 18. 18 is divisible by 9, so we know that 4248 is divisible by 9