Q: What are the factor combinations of the number 367,003?

 A:
Positive:   1 x 3670037 x 5242913 x 2823137 x 991991 x 4033109 x 3367259 x 1417481 x 763
Negative: -1 x -367003-7 x -52429-13 x -28231-37 x -9919-91 x -4033-109 x -3367-259 x -1417-481 x -763


How do I find the factor combinations of the number 367,003?

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 367,003, 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.

1 367,003
-1 -367,003

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 367,003.

Example:
1 x 367,003 = 367,003
and
-1 x -367,003 = 367,003
Notice both answers equal 367,003

With that explanation out of the way, let's continue. Next, we take the number 367,003 and divide it by 2:

367,003 ÷ 2 = 183,501.5

If the quotient is a whole number, then 2 and 183,501.5 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:

1 367,003
-1 -367,003

Now, we try dividing 367,003 by 3:

367,003 ÷ 3 = 122,334.3333

If the quotient is a whole number, then 3 and 122,334.3333 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:

1 367,003
-1 -367,003

Let's try dividing by 4:

367,003 ÷ 4 = 91,750.75

If the quotient is a whole number, then 4 and 91,750.75 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:

1 367,003
-1 367,003
Keep dividing by the next highest number until you cannot divide anymore.

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

171337911092594817631,4173,3674,0339,91928,23152,429367,003
-1-7-13-37-91-109-259-481-763-1,417-3,367-4,033-9,919-28,231-52,429-367,003

More Examples

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