Q: What are the factor combinations of the number 46,213,601?

 A:
Positive:   1 x 462136017 x 660194323 x 200928741 x 1127161161 x 287041287 x 161023943 x 490076601 x 7001
Negative: -1 x -46213601-7 x -6601943-23 x -2009287-41 x -1127161-161 x -287041-287 x -161023-943 x -49007-6601 x -7001


How do I find the factor combinations of the number 46,213,601?

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 46,213,601, 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 46,213,601
-1 -46,213,601

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 46,213,601.

Example:
1 x 46,213,601 = 46,213,601
and
-1 x -46,213,601 = 46,213,601
Notice both answers equal 46,213,601

With that explanation out of the way, let's continue. Next, we take the number 46,213,601 and divide it by 2:

46,213,601 ÷ 2 = 23,106,800.5

If the quotient is a whole number, then 2 and 23,106,800.5 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 46,213,601
-1 -46,213,601

Now, we try dividing 46,213,601 by 3:

46,213,601 ÷ 3 = 15,404,533.6667

If the quotient is a whole number, then 3 and 15,404,533.6667 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 46,213,601
-1 -46,213,601

Let's try dividing by 4:

46,213,601 ÷ 4 = 11,553,400.25

If the quotient is a whole number, then 4 and 11,553,400.25 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 46,213,601
-1 46,213,601
Keep dividing by the next highest number until you cannot divide anymore.

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

1723411612879436,6017,00149,007161,023287,0411,127,1612,009,2876,601,94346,213,601
-1-7-23-41-161-287-943-6,601-7,001-49,007-161,023-287,041-1,127,161-2,009,287-6,601,943-46,213,601

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