Q: What are the factor combinations of the number 14,031,025?

 A:
Positive:   1 x 140310255 x 280620519 x 73847525 x 56124195 x 147695109 x 128725271 x 51775475 x 29539545 x 257451355 x 103552071 x 67752725 x 5149
Negative: -1 x -14031025-5 x -2806205-19 x -738475-25 x -561241-95 x -147695-109 x -128725-271 x -51775-475 x -29539-545 x -25745-1355 x -10355-2071 x -6775-2725 x -5149


How do I find the factor combinations of the number 14,031,025?

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 14,031,025, 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 14,031,025
-1 -14,031,025

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 14,031,025.

Example:
1 x 14,031,025 = 14,031,025
and
-1 x -14,031,025 = 14,031,025
Notice both answers equal 14,031,025

With that explanation out of the way, let's continue. Next, we take the number 14,031,025 and divide it by 2:

14,031,025 ÷ 2 = 7,015,512.5

If the quotient is a whole number, then 2 and 7,015,512.5 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 14,031,025
-1 -14,031,025

Now, we try dividing 14,031,025 by 3:

14,031,025 ÷ 3 = 4,677,008.3333

If the quotient is a whole number, then 3 and 4,677,008.3333 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 14,031,025
-1 -14,031,025

Let's try dividing by 4:

14,031,025 ÷ 4 = 3,507,756.25

If the quotient is a whole number, then 4 and 3,507,756.25 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 14,031,025
-1 14,031,025
Keep dividing by the next highest number until you cannot divide anymore.

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

151925951092714755451,3552,0712,7255,1496,77510,35525,74529,53951,775128,725147,695561,241738,4752,806,20514,031,025
-1-5-19-25-95-109-271-475-545-1,355-2,071-2,725-5,149-6,775-10,355-25,745-29,539-51,775-128,725-147,695-561,241-738,475-2,806,205-14,031,025

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