Q: What are the factor combinations of the number 90,457,746?

 A:
Positive:   1 x 904577462 x 452288733 x 301525826 x 1507629119 x 476093438 x 238046757 x 1586978114 x 793489
Negative: -1 x -90457746-2 x -45228873-3 x -30152582-6 x -15076291-19 x -4760934-38 x -2380467-57 x -1586978-114 x -793489


How do I find the factor combinations of the number 90,457,746?

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 90,457,746, 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 90,457,746
-1 -90,457,746

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 90,457,746.

Example:
1 x 90,457,746 = 90,457,746
and
-1 x -90,457,746 = 90,457,746
Notice both answers equal 90,457,746

With that explanation out of the way, let's continue. Next, we take the number 90,457,746 and divide it by 2:

90,457,746 ÷ 2 = 45,228,873

If the quotient is a whole number, then 2 and 45,228,873 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 45,228,873 90,457,746
-1 -2 -45,228,873 -90,457,746

Now, we try dividing 90,457,746 by 3:

90,457,746 ÷ 3 = 30,152,582

If the quotient is a whole number, then 3 and 30,152,582 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 30,152,582 45,228,873 90,457,746
-1 -2 -3 -30,152,582 -45,228,873 -90,457,746

Let's try dividing by 4:

90,457,746 ÷ 4 = 22,614,436.5

If the quotient is a whole number, then 4 and 22,614,436.5 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 2 3 30,152,582 45,228,873 90,457,746
-1 -2 -3 -30,152,582 -45,228,873 90,457,746
Keep dividing by the next highest number until you cannot divide anymore.

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

1236193857114793,4891,586,9782,380,4674,760,93415,076,29130,152,58245,228,87390,457,746
-1-2-3-6-19-38-57-114-793,489-1,586,978-2,380,467-4,760,934-15,076,291-30,152,582-45,228,873-90,457,746

More Examples

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