Q: What are the factor combinations of the number 123,512,521?

 A:
Positive:   1 x 12351252111 x 1122841119 x 6500659209 x 590969383 x 3224871543 x 800474213 x 293177277 x 16973
Negative: -1 x -123512521-11 x -11228411-19 x -6500659-209 x -590969-383 x -322487-1543 x -80047-4213 x -29317-7277 x -16973


How do I find the factor combinations of the number 123,512,521?

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 123,512,521, 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.

1 123,512,521
-1 -123,512,521

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 123,512,521.

Example:
1 x 123,512,521 = 123,512,521
and
-1 x -123,512,521 = 123,512,521
Notice both answers equal 123,512,521

With that explanation out of the way, let's continue. Next, we take the number 123,512,521 and divide it by 2:

123,512,521 ÷ 2 = 61,756,260.5

If the quotient is a whole number, then 2 and 61,756,260.5 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:

1 123,512,521
-1 -123,512,521

Now, we try dividing 123,512,521 by 3:

123,512,521 ÷ 3 = 41,170,840.3333

If the quotient is a whole number, then 3 and 41,170,840.3333 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:

1 123,512,521
-1 -123,512,521

Let's try dividing by 4:

123,512,521 ÷ 4 = 30,878,130.25

If the quotient is a whole number, then 4 and 30,878,130.25 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:

1 123,512,521
-1 123,512,521
Keep dividing by the next highest number until you cannot divide anymore.

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

111192093831,5434,2137,27716,97329,31780,047322,487590,9696,500,65911,228,411123,512,521
-1-11-19-209-383-1,543-4,213-7,277-16,973-29,317-80,047-322,487-590,969-6,500,659-11,228,411-123,512,521

More Examples

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