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Question

# Use the divisibility tests to determine whether the following numbers are divisible by 2, 3, 4, 5, 6, 9 or 11. (i) 280

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Solution

## We can observe that the number has the digit 0 in its units place.If a number has either 0 or 5 in its units place, then the number is divisible by 5. Also, if a number has the digits 0, 2, 4, 6 or 8 in its units place, then the number is divisible by 2. So, the number 280 is divisible by both 2 and 5.The number formed by the digits at the tens and units places is 80, which is divisible by 4.If the number formed by the digits in the tens and units places of a number is divisible by 4, then the number is divisible by 4. So, the number 280 is divisible by 4.As the sum of the digits is 2+8+0=10 which is not a multiple of 3,therefore 280 is not divisible by 3,6 or 9.Also, sum of alternating digits is not a multiple of 0. Therefore, 280 is not divisible by 11.Hence, the number 280 is divisible by 2, 4 and 5.

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