Q: What are the factor combinations of the number 712,520,225?

 A:
Positive:   1 x 7125202255 x 14250404525 x 285008091039 x 6857755195 x 13715525975 x 27431
Negative: -1 x -712520225-5 x -142504045-25 x -28500809-1039 x -685775-5195 x -137155-25975 x -27431


How do I find the factor combinations of the number 712,520,225?

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 712,520,225, 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.

1 712,520,225
-1 -712,520,225

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 712,520,225.

Example:
1 x 712,520,225 = 712,520,225
and
-1 x -712,520,225 = 712,520,225
Notice both answers equal 712,520,225

With that explanation out of the way, let's continue. Next, we take the number 712,520,225 and divide it by 2:

712,520,225 ÷ 2 = 356,260,112.5

If the quotient is a whole number, then 2 and 356,260,112.5 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:

1 712,520,225
-1 -712,520,225

Now, we try dividing 712,520,225 by 3:

712,520,225 ÷ 3 = 237,506,741.6667

If the quotient is a whole number, then 3 and 237,506,741.6667 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:

1 712,520,225
-1 -712,520,225

Let's try dividing by 4:

712,520,225 ÷ 4 = 178,130,056.25

If the quotient is a whole number, then 4 and 178,130,056.25 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:

1 712,520,225
-1 712,520,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15251,0395,19525,97527,431137,155685,77528,500,809142,504,045712,520,225
-1-5-25-1,039-5,195-25,975-27,431-137,155-685,775-28,500,809-142,504,045-712,520,225

More Examples

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