Q: What are the factor combinations of the number 1,525,121?

 A:
Positive:   1 x 152512113 x 11731717 x 8971367 x 22763103 x 14807221 x 6901871 x 17511139 x 1339
Negative: -1 x -1525121-13 x -117317-17 x -89713-67 x -22763-103 x -14807-221 x -6901-871 x -1751-1139 x -1339


How do I find the factor combinations of the number 1,525,121?

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 1,525,121, 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 1,525,121
-1 -1,525,121

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 1,525,121.

Example:
1 x 1,525,121 = 1,525,121
and
-1 x -1,525,121 = 1,525,121
Notice both answers equal 1,525,121

With that explanation out of the way, let's continue. Next, we take the number 1,525,121 and divide it by 2:

1,525,121 ÷ 2 = 762,560.5

If the quotient is a whole number, then 2 and 762,560.5 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 1,525,121
-1 -1,525,121

Now, we try dividing 1,525,121 by 3:

1,525,121 ÷ 3 = 508,373.6667

If the quotient is a whole number, then 3 and 508,373.6667 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 1,525,121
-1 -1,525,121

Let's try dividing by 4:

1,525,121 ÷ 4 = 381,280.25

If the quotient is a whole number, then 4 and 381,280.25 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 1,525,121
-1 1,525,121
Keep dividing by the next highest number until you cannot divide anymore.

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

11317671032218711,1391,3391,7516,90114,80722,76389,713117,3171,525,121
-1-13-17-67-103-221-871-1,139-1,339-1,751-6,901-14,807-22,763-89,713-117,317-1,525,121

More Examples

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