Q: What are the factor combinations of the number 403,210,032?

 A:
Positive:   1 x 4032100322 x 2016050163 x 1344033444 x 1008025086 x 672016728 x 5040125412 x 3360083616 x 2520062724 x 1680041848 x 8400209463 x 870864926 x 4354321389 x 2902881852 x 2177162778 x 1451443704 x 1088585556 x 725727408 x 5442911112 x 3628618143 x 22224
Negative: -1 x -403210032-2 x -201605016-3 x -134403344-4 x -100802508-6 x -67201672-8 x -50401254-12 x -33600836-16 x -25200627-24 x -16800418-48 x -8400209-463 x -870864-926 x -435432-1389 x -290288-1852 x -217716-2778 x -145144-3704 x -108858-5556 x -72572-7408 x -54429-11112 x -36286-18143 x -22224


How do I find the factor combinations of the number 403,210,032?

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 403,210,032, 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.

1 403,210,032
-1 -403,210,032

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 403,210,032.

Example:
1 x 403,210,032 = 403,210,032
and
-1 x -403,210,032 = 403,210,032
Notice both answers equal 403,210,032

With that explanation out of the way, let's continue. Next, we take the number 403,210,032 and divide it by 2:

403,210,032 ÷ 2 = 201,605,016

If the quotient is a whole number, then 2 and 201,605,016 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 2 201,605,016 403,210,032
-1 -2 -201,605,016 -403,210,032

Now, we try dividing 403,210,032 by 3:

403,210,032 ÷ 3 = 134,403,344

If the quotient is a whole number, then 3 and 134,403,344 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 3 134,403,344 201,605,016 403,210,032
-1 -2 -3 -134,403,344 -201,605,016 -403,210,032

Let's try dividing by 4:

403,210,032 ÷ 4 = 100,802,508

If the quotient is a whole number, then 4 and 100,802,508 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 4 100,802,508 134,403,344 201,605,016 403,210,032
-1 -2 -3 -4 -100,802,508 -134,403,344 -201,605,016 403,210,032
Keep dividing by the next highest number until you cannot divide anymore.

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

123468121624484639261,3891,8522,7783,7045,5567,40811,11218,14322,22436,28654,42972,572108,858145,144217,716290,288435,432870,8648,400,20916,800,41825,200,62733,600,83650,401,25467,201,672100,802,508134,403,344201,605,016403,210,032
-1-2-3-4-6-8-12-16-24-48-463-926-1,389-1,852-2,778-3,704-5,556-7,408-11,112-18,143-22,224-36,286-54,429-72,572-108,858-145,144-217,716-290,288-435,432-870,864-8,400,209-16,800,418-25,200,627-33,600,836-50,401,254-67,201,672-100,802,508-134,403,344-201,605,016-403,210,032

More Examples

Here are some more numbers to try:

403,210,030403,210,031403,210,033403,210,034
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