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Rules for spotting factors

We often need to spot the factors for a higher number. How can we do this without doing the division sums?

For some numbers, its easy to spot. How can you tell if 5 is a factor of your number?

That’s easy. If the last digit of the number is a 0 or 5, then 5 is a factor. If it doesn’t, then 5 is not a factor

5 is a factor of 670 and 1225. It is not a factor of 234 or 1352.

Is 2 a factor? That’s easy in a similar way. The last digit needs to be a 0, 2, 4, 6 or 8.  The even numbers, of course. 2 is a factor of even numbers. Its not a factor of odd numbers.

Is 3 a factor?  Or 9?  For these possible factors we don’t just look at the last digit, but we add up all the digits in the number. If they come to a known multiple of 3, then 3 is a factor. If they come to a known factor of 9 then 9 is a factor.

So 4524 – add up the digits  4 + 5 + 2 + 4 = 15 – 15 is 3 x 5 so 3 is a factor of 4524, but 9 is not.

But 4527  4 + 5 + 2 + 7 = 18  and 9 is a factor of 18, so it is also a factor of 4527.

Note the pattern also holds for 15 and 18 – I used our knowledge of 3 x 5 = 15 and 2 x 9 = 18 above,  but also 1 + 5 = 6 and 1 + 8 = 9.

How do I know if 6 is a factor?  Use both rules above.  If 2 is a factor and 3 is a factor, then so is 6.