Factors

Factors of a number are the numbers that exactly divide that number, leaving no remainders. Let’s look at how to find the factors of a given number.

For example, the factors of 10 are 1, 2, 5, and 10. The factors of 12 are 1, 2, 3, 4, 6, and 12, since the division of 12 by either 1, 2, 3, 4, 6, or 12 results in whole numbers.

Finding Factors of Larger Numbers

With larger numbers, we have to be careful when finding the factors, as we can easily make mistakes like missing a factor or including numbers which are not factors. Let’s look at an example.

Example

Find the factors of 108.

To find the factors of 108, we can create a table like the one below:

FactorsMultiplication
1108
254
336
427
618
912

1. Start with the smallest factor, which is always 1. Write 1 in the left column and 108 in the right column, since 1 \times 108 = 108.

2. Check each integer in ascending order to see if it is a factor. If it is, write the factor in the left column and the result of the division in the right column.

3. Continue this process until a factor repeats itself. In this case, we stop after writing 9 and 12, since 12 is already in the right column.

Now, we can list down the factors of 108:

Start from the left-hand column, starting from 1, and make your way down: 1, 2, 3, 4, 6, and 9. After this, move to the right-hand column, and make your way up: 12, 18, 27, 36, 54, and 108.

Therefore, the factors of 108 are:

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.

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