Q: What are the factor combinations of the number 458,951?

 A:
Positive:   1 x 45895173 x 6287
Negative: -1 x -458951-73 x -6287


How do I find the factor combinations of the number 458,951?

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 458,951, 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.

1 458,951
-1 -458,951

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 458,951.

Example:
1 x 458,951 = 458,951
and
-1 x -458,951 = 458,951
Notice both answers equal 458,951

With that explanation out of the way, let's continue. Next, we take the number 458,951 and divide it by 2:

458,951 ÷ 2 = 229,475.5

If the quotient is a whole number, then 2 and 229,475.5 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:

1 458,951
-1 -458,951

Now, we try dividing 458,951 by 3:

458,951 ÷ 3 = 152,983.6667

If the quotient is a whole number, then 3 and 152,983.6667 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:

1 458,951
-1 -458,951

Let's try dividing by 4:

458,951 ÷ 4 = 114,737.75

If the quotient is a whole number, then 4 and 114,737.75 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:

1 458,951
-1 458,951
Keep dividing by the next highest number until you cannot divide anymore.

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

1736,287458,951
-1-73-6,287-458,951

More Examples

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