Q: What are the factor combinations of the number 43,321,025?

 A:
Positive:   1 x 433210255 x 866420511 x 393827525 x 173284155 x 787655121 x 358025275 x 157531605 x 716053025 x 14321
Negative: -1 x -43321025-5 x -8664205-11 x -3938275-25 x -1732841-55 x -787655-121 x -358025-275 x -157531-605 x -71605-3025 x -14321


How do I find the factor combinations of the number 43,321,025?

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 43,321,025, 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 43,321,025
-1 -43,321,025

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 43,321,025.

Example:
1 x 43,321,025 = 43,321,025
and
-1 x -43,321,025 = 43,321,025
Notice both answers equal 43,321,025

With that explanation out of the way, let's continue. Next, we take the number 43,321,025 and divide it by 2:

43,321,025 ÷ 2 = 21,660,512.5

If the quotient is a whole number, then 2 and 21,660,512.5 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 43,321,025
-1 -43,321,025

Now, we try dividing 43,321,025 by 3:

43,321,025 ÷ 3 = 14,440,341.6667

If the quotient is a whole number, then 3 and 14,440,341.6667 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 43,321,025
-1 -43,321,025

Let's try dividing by 4:

43,321,025 ÷ 4 = 10,830,256.25

If the quotient is a whole number, then 4 and 10,830,256.25 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 43,321,025
-1 43,321,025
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551212756053,02514,32171,605157,531358,025787,6551,732,8413,938,2758,664,20543,321,025
-1-5-11-25-55-121-275-605-3,025-14,321-71,605-157,531-358,025-787,655-1,732,841-3,938,275-8,664,205-43,321,025

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