Q: What are the factor combinations of the number 51,320,521?

 A:
Positive:   1 x 513205217 x 733150323 x 2231327151 x 339871161 x 3187611057 x 485532111 x 243113473 x 14777
Negative: -1 x -51320521-7 x -7331503-23 x -2231327-151 x -339871-161 x -318761-1057 x -48553-2111 x -24311-3473 x -14777


How do I find the factor combinations of the number 51,320,521?

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 51,320,521, 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 51,320,521
-1 -51,320,521

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 51,320,521.

Example:
1 x 51,320,521 = 51,320,521
and
-1 x -51,320,521 = 51,320,521
Notice both answers equal 51,320,521

With that explanation out of the way, let's continue. Next, we take the number 51,320,521 and divide it by 2:

51,320,521 ÷ 2 = 25,660,260.5

If the quotient is a whole number, then 2 and 25,660,260.5 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 51,320,521
-1 -51,320,521

Now, we try dividing 51,320,521 by 3:

51,320,521 ÷ 3 = 17,106,840.3333

If the quotient is a whole number, then 3 and 17,106,840.3333 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 51,320,521
-1 -51,320,521

Let's try dividing by 4:

51,320,521 ÷ 4 = 12,830,130.25

If the quotient is a whole number, then 4 and 12,830,130.25 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 51,320,521
-1 51,320,521
Keep dividing by the next highest number until you cannot divide anymore.

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

17231511611,0572,1113,47314,77724,31148,553318,761339,8712,231,3277,331,50351,320,521
-1-7-23-151-161-1,057-2,111-3,473-14,777-24,311-48,553-318,761-339,871-2,231,327-7,331,503-51,320,521

More Examples

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