Q: What are the factor combinations of the number 354,851?

 A:
Positive:   1 x 3548517 x 50693163 x 2177311 x 1141
Negative: -1 x -354851-7 x -50693-163 x -2177-311 x -1141


How do I find the factor combinations of the number 354,851?

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 354,851, 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.

1 354,851
-1 -354,851

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 354,851.

Example:
1 x 354,851 = 354,851
and
-1 x -354,851 = 354,851
Notice both answers equal 354,851

With that explanation out of the way, let's continue. Next, we take the number 354,851 and divide it by 2:

354,851 ÷ 2 = 177,425.5

If the quotient is a whole number, then 2 and 177,425.5 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:

1 354,851
-1 -354,851

Now, we try dividing 354,851 by 3:

354,851 ÷ 3 = 118,283.6667

If the quotient is a whole number, then 3 and 118,283.6667 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:

1 354,851
-1 -354,851

Let's try dividing by 4:

354,851 ÷ 4 = 88,712.75

If the quotient is a whole number, then 4 and 88,712.75 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:

1 354,851
-1 354,851
Keep dividing by the next highest number until you cannot divide anymore.

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

171633111,1412,17750,693354,851
-1-7-163-311-1,141-2,177-50,693-354,851

More Examples

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