Q: What are the factor combinations of the number 3,502,139?

 A:
Positive:   1 x 3502139257 x 13627
Negative: -1 x -3502139-257 x -13627


How do I find the factor combinations of the number 3,502,139?

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 3,502,139, 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 3,502,139
-1 -3,502,139

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 3,502,139.

Example:
1 x 3,502,139 = 3,502,139
and
-1 x -3,502,139 = 3,502,139
Notice both answers equal 3,502,139

With that explanation out of the way, let's continue. Next, we take the number 3,502,139 and divide it by 2:

3,502,139 ÷ 2 = 1,751,069.5

If the quotient is a whole number, then 2 and 1,751,069.5 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 3,502,139
-1 -3,502,139

Now, we try dividing 3,502,139 by 3:

3,502,139 ÷ 3 = 1,167,379.6667

If the quotient is a whole number, then 3 and 1,167,379.6667 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 3,502,139
-1 -3,502,139

Let's try dividing by 4:

3,502,139 ÷ 4 = 875,534.75

If the quotient is a whole number, then 4 and 875,534.75 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 3,502,139
-1 3,502,139
Keep dividing by the next highest number until you cannot divide anymore.

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

125713,6273,502,139
-1-257-13,627-3,502,139

More Examples

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