Q: What are the factor combinations of the number 372,505?

 A:
Positive:   1 x 3725055 x 745017 x 5321529 x 1284535 x 10643145 x 2569203 x 1835367 x 1015
Negative: -1 x -372505-5 x -74501-7 x -53215-29 x -12845-35 x -10643-145 x -2569-203 x -1835-367 x -1015


How do I find the factor combinations of the number 372,505?

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 372,505, 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.

1 372,505
-1 -372,505

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 372,505.

Example:
1 x 372,505 = 372,505
and
-1 x -372,505 = 372,505
Notice both answers equal 372,505

With that explanation out of the way, let's continue. Next, we take the number 372,505 and divide it by 2:

372,505 ÷ 2 = 186,252.5

If the quotient is a whole number, then 2 and 186,252.5 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:

1 372,505
-1 -372,505

Now, we try dividing 372,505 by 3:

372,505 ÷ 3 = 124,168.3333

If the quotient is a whole number, then 3 and 124,168.3333 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:

1 372,505
-1 -372,505

Let's try dividing by 4:

372,505 ÷ 4 = 93,126.25

If the quotient is a whole number, then 4 and 93,126.25 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:

1 372,505
-1 372,505
Keep dividing by the next highest number until you cannot divide anymore.

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

15729351452033671,0151,8352,56910,64312,84553,21574,501372,505
-1-5-7-29-35-145-203-367-1,015-1,835-2,569-10,643-12,845-53,215-74,501-372,505

More Examples

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