Q: What are the factor combinations of the number 1,506,631?

 A:
Positive:   1 x 15066317 x 21523331 x 4860153 x 28427131 x 11501217 x 6943371 x 4061917 x 1643
Negative: -1 x -1506631-7 x -215233-31 x -48601-53 x -28427-131 x -11501-217 x -6943-371 x -4061-917 x -1643


How do I find the factor combinations of the number 1,506,631?

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 1,506,631, 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 1,506,631
-1 -1,506,631

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 1,506,631.

Example:
1 x 1,506,631 = 1,506,631
and
-1 x -1,506,631 = 1,506,631
Notice both answers equal 1,506,631

With that explanation out of the way, let's continue. Next, we take the number 1,506,631 and divide it by 2:

1,506,631 ÷ 2 = 753,315.5

If the quotient is a whole number, then 2 and 753,315.5 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 1,506,631
-1 -1,506,631

Now, we try dividing 1,506,631 by 3:

1,506,631 ÷ 3 = 502,210.3333

If the quotient is a whole number, then 3 and 502,210.3333 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 1,506,631
-1 -1,506,631

Let's try dividing by 4:

1,506,631 ÷ 4 = 376,657.75

If the quotient is a whole number, then 4 and 376,657.75 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 1,506,631
-1 1,506,631
Keep dividing by the next highest number until you cannot divide anymore.

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

1731531312173719171,6434,0616,94311,50128,42748,601215,2331,506,631
-1-7-31-53-131-217-371-917-1,643-4,061-6,943-11,501-28,427-48,601-215,233-1,506,631

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