Write down all the factors of 24.
First, let’s remind ourselves what is meant by the word “factors.” The factors of a number are the other numbers or, more specifically, they must be integers, that is, whole numbers, which can be multiplied together to give that number. So we’re looking for integers which multiply together to give 24.
Well, any number can be written as the product of one and itself. So 24 is equal to one multiplied by 24, which means that both one and 24 are factors of 24. 24 is an even number, which means that two is also a factor of 24. In fact, two multiplied by 12 gives 24. So two and 12 are both factors of 24.
We should also recognize 24 as being in the three times table. 24 is equal to three multiplied by eight. So both three and eight are factors of 24. 24 is also in our four times table. It’s equal to four multiplied by six. So four and six are both factors of 24.
We’ve now checked all of the integers from one to four and found that they are indeed factors of 24. What about the next integer, five? Well, 24 isn’t in the five times table. And we know this because 24 doesn’t end in either a zero or a five. Therefore, five is not a factor of 24.
The next integer to check would be six. But notice that six already appears in our list of factors, because it was paired with four. 24 is equal to four times six but is also equal to six times four. We’ve already included this factor pair. And if we were to continue, we would find the same factors but in the opposite order. So we’d find eight multiplied by three and then 12 multiplied by two and then 24 multiplied by one. We don’t need to include these factors the other way round. So our search for factors of 24 stops here.
It’s usual, although not absolutely essential, to write our list of factors in ascending order. That’s increasing order. So our list of factors of 24 is one, two, three, four, six, eight, 12, 24.