Q: What are the factor combinations of the number 900,396?

 A:
Positive:   1 x 9003962 x 4501983 x 3001324 x 2250996 x 1500667 x 1286289 x 10004412 x 7503314 x 6431418 x 5002221 x 4287627 x 3334828 x 3215736 x 2501142 x 2143854 x 1667463 x 1429281 x 1111684 x 10719108 x 8337126 x 7146162 x 5558189 x 4764252 x 3573324 x 2779378 x 2382397 x 2268567 x 1588756 x 1191794 x 1134
Negative: -1 x -900396-2 x -450198-3 x -300132-4 x -225099-6 x -150066-7 x -128628-9 x -100044-12 x -75033-14 x -64314-18 x -50022-21 x -42876-27 x -33348-28 x -32157-36 x -25011-42 x -21438-54 x -16674-63 x -14292-81 x -11116-84 x -10719-108 x -8337-126 x -7146-162 x -5558-189 x -4764-252 x -3573-324 x -2779-378 x -2382-397 x -2268-567 x -1588-756 x -1191-794 x -1134


How do I find the factor combinations of the number 900,396?

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 900,396, 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.

1 900,396
-1 -900,396

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 900,396.

Example:
1 x 900,396 = 900,396
and
-1 x -900,396 = 900,396
Notice both answers equal 900,396

With that explanation out of the way, let's continue. Next, we take the number 900,396 and divide it by 2:

900,396 ÷ 2 = 450,198

If the quotient is a whole number, then 2 and 450,198 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 2 450,198 900,396
-1 -2 -450,198 -900,396

Now, we try dividing 900,396 by 3:

900,396 ÷ 3 = 300,132

If the quotient is a whole number, then 3 and 300,132 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 3 300,132 450,198 900,396
-1 -2 -3 -300,132 -450,198 -900,396

Let's try dividing by 4:

900,396 ÷ 4 = 225,099

If the quotient is a whole number, then 4 and 225,099 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 4 225,099 300,132 450,198 900,396
-1 -2 -3 -4 -225,099 -300,132 -450,198 900,396
Keep dividing by the next highest number until you cannot divide anymore.

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

12346791214182127283642546381841081261621892523243783975677567941,1341,1911,5882,2682,3822,7793,5734,7645,5587,1468,33710,71911,11614,29216,67421,43825,01132,15733,34842,87650,02264,31475,033100,044128,628150,066225,099300,132450,198900,396
-1-2-3-4-6-7-9-12-14-18-21-27-28-36-42-54-63-81-84-108-126-162-189-252-324-378-397-567-756-794-1,134-1,191-1,588-2,268-2,382-2,779-3,573-4,764-5,558-7,146-8,337-10,719-11,116-14,292-16,674-21,438-25,011-32,157-33,348-42,876-50,022-64,314-75,033-100,044-128,628-150,066-225,099-300,132-450,198-900,396

More Examples

Here are some more numbers to try:

900,394900,395900,397900,398
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