Q: What are the factor combinations of the number 1,547?

 A:
Positive:   1 x 15477 x 22113 x 11917 x 91
Negative: -1 x -1547-7 x -221-13 x -119-17 x -91


How do I find the factor combinations of the number 1,547?

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 divisors of larger numbers. To find the factor combinations of the number 1,547, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

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. Then, below that, write the numbers as a negative as well.

1 1,547
-1 -1,547

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 1,547.

Example:
1 x 1,547 = 1,547
and
-1 x -1,547 = 1,547
Notice both answers equal 1,547

With that explanation out of the way, let's continue. Next, we take the number 1,547 and divide it by 2:

1,547 ÷ 2 = 773.5

If the quotient is a whole number, then 2 and 773.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 1,547
-1 -1,547

Now, we try dividing 1,547 by 3:

1,547 ÷ 3 = 515.6667

If the quotient is a whole number, then 3 and 515.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 1,547
-1 -1,547

Let's try dividing by 4:

1,547 ÷ 4 = 386.75

If the quotient is a whole number, then 4 and 386.75 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 1,547
-1 1,547
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

171317911192211,547
-1-7-13-17-91-119-221-1,547

More Examples

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