Q: What are the factor combinations of the number 46,121,125?

 A:
Positive:   1 x 461211255 x 922422525 x 184484567 x 688375125 x 368969335 x 1376751675 x 275355507 x 8375
Negative: -1 x -46121125-5 x -9224225-25 x -1844845-67 x -688375-125 x -368969-335 x -137675-1675 x -27535-5507 x -8375


How do I find the factor combinations of the number 46,121,125?

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 46,121,125, 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 46,121,125
-1 -46,121,125

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 46,121,125.

Example:
1 x 46,121,125 = 46,121,125
and
-1 x -46,121,125 = 46,121,125
Notice both answers equal 46,121,125

With that explanation out of the way, let's continue. Next, we take the number 46,121,125 and divide it by 2:

46,121,125 ÷ 2 = 23,060,562.5

If the quotient is a whole number, then 2 and 23,060,562.5 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 46,121,125
-1 -46,121,125

Now, we try dividing 46,121,125 by 3:

46,121,125 ÷ 3 = 15,373,708.3333

If the quotient is a whole number, then 3 and 15,373,708.3333 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 46,121,125
-1 -46,121,125

Let's try dividing by 4:

46,121,125 ÷ 4 = 11,530,281.25

If the quotient is a whole number, then 4 and 11,530,281.25 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 46,121,125
-1 46,121,125
Keep dividing by the next highest number until you cannot divide anymore.

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

1525671253351,6755,5078,37527,535137,675368,969688,3751,844,8459,224,22546,121,125
-1-5-25-67-125-335-1,675-5,507-8,375-27,535-137,675-368,969-688,375-1,844,845-9,224,225-46,121,125

More Examples

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