Q: What are the factor combinations of the number 974,428?

 A:
Positive:   1 x 9744282 x 4872144 x 2436077 x 13920413 x 7495614 x 6960226 x 3747828 x 3480152 x 1873991 x 10708182 x 5354364 x 2677
Negative: -1 x -974428-2 x -487214-4 x -243607-7 x -139204-13 x -74956-14 x -69602-26 x -37478-28 x -34801-52 x -18739-91 x -10708-182 x -5354-364 x -2677


How do I find the factor combinations of the number 974,428?

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 974,428, 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.

1 974,428
-1 -974,428

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 974,428.

Example:
1 x 974,428 = 974,428
and
-1 x -974,428 = 974,428
Notice both answers equal 974,428

With that explanation out of the way, let's continue. Next, we take the number 974,428 and divide it by 2:

974,428 ÷ 2 = 487,214

If the quotient is a whole number, then 2 and 487,214 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 2 487,214 974,428
-1 -2 -487,214 -974,428

Now, we try dividing 974,428 by 3:

974,428 ÷ 3 = 324,809.3333

If the quotient is a whole number, then 3 and 324,809.3333 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 2 487,214 974,428
-1 -2 -487,214 -974,428

Let's try dividing by 4:

974,428 ÷ 4 = 243,607

If the quotient is a whole number, then 4 and 243,607 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 4 243,607 487,214 974,428
-1 -2 -4 -243,607 -487,214 974,428
Keep dividing by the next highest number until you cannot divide anymore.

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

12471314262852911823642,6775,35410,70818,73934,80137,47869,60274,956139,204243,607487,214974,428
-1-2-4-7-13-14-26-28-52-91-182-364-2,677-5,354-10,708-18,739-34,801-37,478-69,602-74,956-139,204-243,607-487,214-974,428

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