Q: What are the factor combinations of the number 902,421?

 A:
Positive:   1 x 9024213 x 3008079 x 10026913 x 6941727 x 3342339 x 2313981 x 11141117 x 7713351 x 2571857 x 1053
Negative: -1 x -902421-3 x -300807-9 x -100269-13 x -69417-27 x -33423-39 x -23139-81 x -11141-117 x -7713-351 x -2571-857 x -1053


How do I find the factor combinations of the number 902,421?

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 902,421, 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.

1 902,421
-1 -902,421

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 902,421.

Example:
1 x 902,421 = 902,421
and
-1 x -902,421 = 902,421
Notice both answers equal 902,421

With that explanation out of the way, let's continue. Next, we take the number 902,421 and divide it by 2:

902,421 ÷ 2 = 451,210.5

If the quotient is a whole number, then 2 and 451,210.5 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:

1 902,421
-1 -902,421

Now, we try dividing 902,421 by 3:

902,421 ÷ 3 = 300,807

If the quotient is a whole number, then 3 and 300,807 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 3 300,807 902,421
-1 -3 -300,807 -902,421

Let's try dividing by 4:

902,421 ÷ 4 = 225,605.25

If the quotient is a whole number, then 4 and 225,605.25 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 3 300,807 902,421
-1 -3 -300,807 902,421
Keep dividing by the next highest number until you cannot divide anymore.

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

139132739811173518571,0532,5717,71311,14123,13933,42369,417100,269300,807902,421
-1-3-9-13-27-39-81-117-351-857-1,053-2,571-7,713-11,141-23,139-33,423-69,417-100,269-300,807-902,421

More Examples

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