Q: What are the factor combinations of the number 406,956?

 A:
Positive:   1 x 4069562 x 2034783 x 1356524 x 1017396 x 6782611 x 3699612 x 3391322 x 1849833 x 1233244 x 924966 x 6166132 x 3083
Negative: -1 x -406956-2 x -203478-3 x -135652-4 x -101739-6 x -67826-11 x -36996-12 x -33913-22 x -18498-33 x -12332-44 x -9249-66 x -6166-132 x -3083


How do I find the factor combinations of the number 406,956?

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 406,956, 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.

1 406,956
-1 -406,956

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 406,956.

Example:
1 x 406,956 = 406,956
and
-1 x -406,956 = 406,956
Notice both answers equal 406,956

With that explanation out of the way, let's continue. Next, we take the number 406,956 and divide it by 2:

406,956 ÷ 2 = 203,478

If the quotient is a whole number, then 2 and 203,478 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

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

1 2 203,478 406,956
-1 -2 -203,478 -406,956

Now, we try dividing 406,956 by 3:

406,956 ÷ 3 = 135,652

If the quotient is a whole number, then 3 and 135,652 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

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

1 2 3 135,652 203,478 406,956
-1 -2 -3 -135,652 -203,478 -406,956

Let's try dividing by 4:

406,956 ÷ 4 = 101,739

If the quotient is a whole number, then 4 and 101,739 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

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

1 2 3 4 101,739 135,652 203,478 406,956
-1 -2 -3 -4 -101,739 -135,652 -203,478 406,956
Keep dividing by the next highest number until you cannot divide anymore.

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

123461112223344661323,0836,1669,24912,33218,49833,91336,99667,826101,739135,652203,478406,956
-1-2-3-4-6-11-12-22-33-44-66-132-3,083-6,166-9,249-12,332-18,498-33,913-36,996-67,826-101,739-135,652-203,478-406,956

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