Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the factors of larger numbers. To find the factors of the number 105, it is easiest to start from the outside in. Here's what we mean:
We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table.
| 1 | 105 |
Next, we take the number 105 and divide it by 2.
In this case, 105 ÷ 2 = 52.5
If the quotient is a whole number, then 2 and 52.5 are factors. Write them in the table below. If the quotient is not a whole number, skip to the next test.
| 1 | 105 |
Now, we try dividing 105 by 3.
105 ÷ 3 = 35
If the quotient is a whole number, then 3 and 35 are factors. Write them in the table below. If the quotient is not a whole number, skip to the next test.
Here is what our table should look like at this step:
| 1 | 3 | 35 | 105 |
Let's try dividing by 4.
105 ÷ 4 = 26.25
If the quotient is a whole number, then 4 and 26.25 are factors. Write them in the table below. If the quotient is not a whole number, skip to the next test.
Here is what our table should look like at this step:
| 1 | 3 | 35 | 105 |
We keep dividing by the next largest number, in this case the number 5. If the quotient of 105 ÷ 5 is a whole number, then 5 and your quotient are factors of the number.
Keep dividing by the next highest number until you cannot divide anymore.
What you will end up with is this table:
| 1 | 3 | 5 | 7 | 15 | 21 | 35 | 105 |
All of the numbers in the table above can be evenly divided into the number 105.
Finally, for your reference, here are all of the divisor combinations of the number 105:
1 x 105
3 x 35
5 x 21
7 x 15
Here are some more numbers to try:
Try the factor calculator