Q: What are the factor combinations of the number 371,988?

 A:
Positive:   1 x 3719882 x 1859943 x 1239964 x 929976 x 619989 x 4133212 x 3099918 x 2066636 x 10333
Negative: -1 x -371988-2 x -185994-3 x -123996-4 x -92997-6 x -61998-9 x -41332-12 x -30999-18 x -20666-36 x -10333


How do I find the factor combinations of the number 371,988?

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 371,988, 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.

1 371,988
-1 -371,988

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 371,988.

Example:
1 x 371,988 = 371,988
and
-1 x -371,988 = 371,988
Notice both answers equal 371,988

With that explanation out of the way, let's continue. Next, we take the number 371,988 and divide it by 2:

371,988 ÷ 2 = 185,994

If the quotient is a whole number, then 2 and 185,994 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 2 185,994 371,988
-1 -2 -185,994 -371,988

Now, we try dividing 371,988 by 3:

371,988 ÷ 3 = 123,996

If the quotient is a whole number, then 3 and 123,996 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 3 123,996 185,994 371,988
-1 -2 -3 -123,996 -185,994 -371,988

Let's try dividing by 4:

371,988 ÷ 4 = 92,997

If the quotient is a whole number, then 4 and 92,997 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 4 92,997 123,996 185,994 371,988
-1 -2 -3 -4 -92,997 -123,996 -185,994 371,988
Keep dividing by the next highest number until you cannot divide anymore.

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

12346912183610,33320,66630,99941,33261,99892,997123,996185,994371,988
-1-2-3-4-6-9-12-18-36-10,333-20,666-30,999-41,332-61,998-92,997-123,996-185,994-371,988

More Examples

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