Q: What are the factor combinations of the number 357,258?

 A:
Positive:   1 x 3572582 x 1786293 x 1190866 x 5954311 x 3247822 x 1623933 x 1082666 x 5413
Negative: -1 x -357258-2 x -178629-3 x -119086-6 x -59543-11 x -32478-22 x -16239-33 x -10826-66 x -5413


How do I find the factor combinations of the number 357,258?

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 357,258, 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.

1 357,258
-1 -357,258

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 357,258.

Example:
1 x 357,258 = 357,258
and
-1 x -357,258 = 357,258
Notice both answers equal 357,258

With that explanation out of the way, let's continue. Next, we take the number 357,258 and divide it by 2:

357,258 ÷ 2 = 178,629

If the quotient is a whole number, then 2 and 178,629 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 178,629 357,258
-1 -2 -178,629 -357,258

Now, we try dividing 357,258 by 3:

357,258 ÷ 3 = 119,086

If the quotient is a whole number, then 3 and 119,086 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 119,086 178,629 357,258
-1 -2 -3 -119,086 -178,629 -357,258

Let's try dividing by 4:

357,258 ÷ 4 = 89,314.5

If the quotient is a whole number, then 4 and 89,314.5 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 2 3 119,086 178,629 357,258
-1 -2 -3 -119,086 -178,629 357,258
Keep dividing by the next highest number until you cannot divide anymore.

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

1236112233665,41310,82616,23932,47859,543119,086178,629357,258
-1-2-3-6-11-22-33-66-5,413-10,826-16,239-32,478-59,543-119,086-178,629-357,258

More Examples

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