Q: What are the factor combinations of the number 351,767?

 A:
Positive:   1 x 35176713 x 27059
Negative: -1 x -351767-13 x -27059


How do I find the factor combinations of the number 351,767?

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 351,767, 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.

1 351,767
-1 -351,767

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 351,767.

Example:
1 x 351,767 = 351,767
and
-1 x -351,767 = 351,767
Notice both answers equal 351,767

With that explanation out of the way, let's continue. Next, we take the number 351,767 and divide it by 2:

351,767 ÷ 2 = 175,883.5

If the quotient is a whole number, then 2 and 175,883.5 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:

1 351,767
-1 -351,767

Now, we try dividing 351,767 by 3:

351,767 ÷ 3 = 117,255.6667

If the quotient is a whole number, then 3 and 117,255.6667 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:

1 351,767
-1 -351,767

Let's try dividing by 4:

351,767 ÷ 4 = 87,941.75

If the quotient is a whole number, then 4 and 87,941.75 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:

1 351,767
-1 351,767
Keep dividing by the next highest number until you cannot divide anymore.

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

11327,059351,767
-1-13-27,059-351,767

More Examples

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