Q: What are the factor combinations of the number 3,521?

 A:
Positive:   1 x 35217 x 503
Negative: -1 x -3521-7 x -503


How do I find the factor combinations of the number 3,521?

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 3,521, 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 3,521
-1 -3,521

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 3,521.

Example:
1 x 3,521 = 3,521
and
-1 x -3,521 = 3,521
Notice both answers equal 3,521

With that explanation out of the way, let's continue. Next, we take the number 3,521 and divide it by 2:

3,521 ÷ 2 = 1,760.5

If the quotient is a whole number, then 2 and 1,760.5 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 3,521
-1 -3,521

Now, we try dividing 3,521 by 3:

3,521 ÷ 3 = 1,173.6667

If the quotient is a whole number, then 3 and 1,173.6667 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 3,521
-1 -3,521

Let's try dividing by 4:

3,521 ÷ 4 = 880.25

If the quotient is a whole number, then 4 and 880.25 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 3,521
-1 3,521
Keep dividing by the next highest number until you cannot divide anymore.

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

175033,521
-1-7-503-3,521

More Examples

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