Q: What are the factor combinations of the number 15,101,125?

 A:
Positive:   1 x 151011255 x 302022513 x 116162525 x 60404565 x 232325125 x 120809325 x 464651625 x 9293
Negative: -1 x -15101125-5 x -3020225-13 x -1161625-25 x -604045-65 x -232325-125 x -120809-325 x -46465-1625 x -9293


How do I find the factor combinations of the number 15,101,125?

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 15,101,125, 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 15,101,125
-1 -15,101,125

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 15,101,125.

Example:
1 x 15,101,125 = 15,101,125
and
-1 x -15,101,125 = 15,101,125
Notice both answers equal 15,101,125

With that explanation out of the way, let's continue. Next, we take the number 15,101,125 and divide it by 2:

15,101,125 ÷ 2 = 7,550,562.5

If the quotient is a whole number, then 2 and 7,550,562.5 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 15,101,125
-1 -15,101,125

Now, we try dividing 15,101,125 by 3:

15,101,125 ÷ 3 = 5,033,708.3333

If the quotient is a whole number, then 3 and 5,033,708.3333 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 15,101,125
-1 -15,101,125

Let's try dividing by 4:

15,101,125 ÷ 4 = 3,775,281.25

If the quotient is a whole number, then 4 and 3,775,281.25 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 15,101,125
-1 15,101,125
Keep dividing by the next highest number until you cannot divide anymore.

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

151325651253251,6259,29346,465120,809232,325604,0451,161,6253,020,22515,101,125
-1-5-13-25-65-125-325-1,625-9,293-46,465-120,809-232,325-604,045-1,161,625-3,020,225-15,101,125

More Examples

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