Q: What are the factor combinations of the number 712,213,153?

 A:
Positive:   1 x 712213153353 x 2017601
Negative: -1 x -712213153-353 x -2017601


How do I find the factor combinations of the number 712,213,153?

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 712,213,153, 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.

1 712,213,153
-1 -712,213,153

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 712,213,153.

Example:
1 x 712,213,153 = 712,213,153
and
-1 x -712,213,153 = 712,213,153
Notice both answers equal 712,213,153

With that explanation out of the way, let's continue. Next, we take the number 712,213,153 and divide it by 2:

712,213,153 ÷ 2 = 356,106,576.5

If the quotient is a whole number, then 2 and 356,106,576.5 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:

1 712,213,153
-1 -712,213,153

Now, we try dividing 712,213,153 by 3:

712,213,153 ÷ 3 = 237,404,384.3333

If the quotient is a whole number, then 3 and 237,404,384.3333 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:

1 712,213,153
-1 -712,213,153

Let's try dividing by 4:

712,213,153 ÷ 4 = 178,053,288.25

If the quotient is a whole number, then 4 and 178,053,288.25 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:

1 712,213,153
-1 712,213,153
Keep dividing by the next highest number until you cannot divide anymore.

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

13532,017,601712,213,153
-1-353-2,017,601-712,213,153

More Examples

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