Q: What are the factor combinations of the number 21,433,225?

 A:
Positive:   1 x 214332255 x 428664511 x 194847525 x 85732955 x 38969559 x 363275275 x 77939295 x 72655649 x 330251321 x 162251475 x 145313245 x 6605
Negative: -1 x -21433225-5 x -4286645-11 x -1948475-25 x -857329-55 x -389695-59 x -363275-275 x -77939-295 x -72655-649 x -33025-1321 x -16225-1475 x -14531-3245 x -6605


How do I find the factor combinations of the number 21,433,225?

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 21,433,225, 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 21,433,225
-1 -21,433,225

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 21,433,225.

Example:
1 x 21,433,225 = 21,433,225
and
-1 x -21,433,225 = 21,433,225
Notice both answers equal 21,433,225

With that explanation out of the way, let's continue. Next, we take the number 21,433,225 and divide it by 2:

21,433,225 ÷ 2 = 10,716,612.5

If the quotient is a whole number, then 2 and 10,716,612.5 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 21,433,225
-1 -21,433,225

Now, we try dividing 21,433,225 by 3:

21,433,225 ÷ 3 = 7,144,408.3333

If the quotient is a whole number, then 3 and 7,144,408.3333 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 21,433,225
-1 -21,433,225

Let's try dividing by 4:

21,433,225 ÷ 4 = 5,358,306.25

If the quotient is a whole number, then 4 and 5,358,306.25 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 21,433,225
-1 21,433,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15112555592752956491,3211,4753,2456,60514,53116,22533,02572,65577,939363,275389,695857,3291,948,4754,286,64521,433,225
-1-5-11-25-55-59-275-295-649-1,321-1,475-3,245-6,605-14,531-16,225-33,025-72,655-77,939-363,275-389,695-857,329-1,948,475-4,286,645-21,433,225

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