Divisibility Tests

Applying Divisibility Tests

Which of the numbers below that are factors (divisors) of 34,971. Use the divisibility rules to decide. Do not divide to figure this out.  

2,   3, 4, 5, 6, 9, 10

Solution:  

The last digit of 34,971 is "1". So we know that 34,971 is not divisible by 2, 5 or 10.

The fact that 34,971 is not divisible by 2 also tells us that it is not divisible by either 4 or 6 (because we need a factor of 2 for either of these).

That leaves us with only 3 and 9 as possible factors (divisors) of 34,971. Both of these divisibility tests require that we look at the sum of the digits, so we sum the digits of 34,971 and get 3 + 4 + 9 + 7 + 1 = 24. The sum of 24 is divisible by 3 but not by 9. Therefore, we conclude that 34,971 is divisible by 3 but not by 9.  

This means that the only number, in the list above, that is a factor (divisor) of 34,971 is 3 and we should only have chosen the numeral 3.

 

Joke or Quote

When you can, count.

Sir Francis Galton (1822-1911)

In J.R. Newman (ed.), The World of Mathematics, New York, Simon and Schuster, 1956

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