Q: What are the factor combinations of the number 400,320,444?

 A:
Positive:   1 x 4003204442 x 2001602223 x 1334401484 x 1000801116 x 6672007412 x 3336003767 x 5974932134 x 2987466201 x 1991644268 x 1493733311 x 1287204402 x 995822622 x 643602804 x 497911933 x 4290681244 x 3218011601 x 2500441866 x 2145343202 x 1250223732 x 1072674803 x 833486404 x 625119606 x 4167419212 x 20837
Negative: -1 x -400320444-2 x -200160222-3 x -133440148-4 x -100080111-6 x -66720074-12 x -33360037-67 x -5974932-134 x -2987466-201 x -1991644-268 x -1493733-311 x -1287204-402 x -995822-622 x -643602-804 x -497911-933 x -429068-1244 x -321801-1601 x -250044-1866 x -214534-3202 x -125022-3732 x -107267-4803 x -83348-6404 x -62511-9606 x -41674-19212 x -20837


How do I find the factor combinations of the number 400,320,444?

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 400,320,444, 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.

1 400,320,444
-1 -400,320,444

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 400,320,444.

Example:
1 x 400,320,444 = 400,320,444
and
-1 x -400,320,444 = 400,320,444
Notice both answers equal 400,320,444

With that explanation out of the way, let's continue. Next, we take the number 400,320,444 and divide it by 2:

400,320,444 ÷ 2 = 200,160,222

If the quotient is a whole number, then 2 and 200,160,222 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 2 200,160,222 400,320,444
-1 -2 -200,160,222 -400,320,444

Now, we try dividing 400,320,444 by 3:

400,320,444 ÷ 3 = 133,440,148

If the quotient is a whole number, then 3 and 133,440,148 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 3 133,440,148 200,160,222 400,320,444
-1 -2 -3 -133,440,148 -200,160,222 -400,320,444

Let's try dividing by 4:

400,320,444 ÷ 4 = 100,080,111

If the quotient is a whole number, then 4 and 100,080,111 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 4 100,080,111 133,440,148 200,160,222 400,320,444
-1 -2 -3 -4 -100,080,111 -133,440,148 -200,160,222 400,320,444
Keep dividing by the next highest number until you cannot divide anymore.

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

1234612671342012683114026228049331,2441,6011,8663,2023,7324,8036,4049,60619,21220,83741,67462,51183,348107,267125,022214,534250,044321,801429,068497,911643,602995,8221,287,2041,493,7331,991,6442,987,4665,974,93233,360,03766,720,074100,080,111133,440,148200,160,222400,320,444
-1-2-3-4-6-12-67-134-201-268-311-402-622-804-933-1,244-1,601-1,866-3,202-3,732-4,803-6,404-9,606-19,212-20,837-41,674-62,511-83,348-107,267-125,022-214,534-250,044-321,801-429,068-497,911-643,602-995,822-1,287,204-1,493,733-1,991,644-2,987,466-5,974,932-33,360,037-66,720,074-100,080,111-133,440,148-200,160,222-400,320,444

More Examples

Here are some more numbers to try:

400,320,442400,320,443400,320,445400,320,446
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