Q: What are the factor combinations of the number 43,512,312?

 A:
Positive:   1 x 435123122 x 217561563 x 145041044 x 108780786 x 72520528 x 543903912 x 362602624 x 1813013419 x 103848838 x 519241257 x 346161676 x 259622514 x 173083352 x 129814327 x 100565028 x 8654
Negative: -1 x -43512312-2 x -21756156-3 x -14504104-4 x -10878078-6 x -7252052-8 x -5439039-12 x -3626026-24 x -1813013-419 x -103848-838 x -51924-1257 x -34616-1676 x -25962-2514 x -17308-3352 x -12981-4327 x -10056-5028 x -8654


How do I find the factor combinations of the number 43,512,312?

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 43,512,312, 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 43,512,312
-1 -43,512,312

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 43,512,312.

Example:
1 x 43,512,312 = 43,512,312
and
-1 x -43,512,312 = 43,512,312
Notice both answers equal 43,512,312

With that explanation out of the way, let's continue. Next, we take the number 43,512,312 and divide it by 2:

43,512,312 ÷ 2 = 21,756,156

If the quotient is a whole number, then 2 and 21,756,156 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 21,756,156 43,512,312
-1 -2 -21,756,156 -43,512,312

Now, we try dividing 43,512,312 by 3:

43,512,312 ÷ 3 = 14,504,104

If the quotient is a whole number, then 3 and 14,504,104 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 14,504,104 21,756,156 43,512,312
-1 -2 -3 -14,504,104 -21,756,156 -43,512,312

Let's try dividing by 4:

43,512,312 ÷ 4 = 10,878,078

If the quotient is a whole number, then 4 and 10,878,078 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 10,878,078 14,504,104 21,756,156 43,512,312
-1 -2 -3 -4 -10,878,078 -14,504,104 -21,756,156 43,512,312
Keep dividing by the next highest number until you cannot divide anymore.

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

12346812244198381,2571,6762,5143,3524,3275,0288,65410,05612,98117,30825,96234,61651,924103,8481,813,0133,626,0265,439,0397,252,05210,878,07814,504,10421,756,15643,512,312
-1-2-3-4-6-8-12-24-419-838-1,257-1,676-2,514-3,352-4,327-5,028-8,654-10,056-12,981-17,308-25,962-34,616-51,924-103,848-1,813,013-3,626,026-5,439,039-7,252,052-10,878,078-14,504,104-21,756,156-43,512,312

More Examples

Here are some more numbers to try:

43,512,31043,512,31143,512,31343,512,314
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