Q: What are the factor combinations of the number 21,018,415?

 A:
Positive:   1 x 210184155 x 420368311 x 191076555 x 382153401 x 52415953 x 220552005 x 104834411 x 4765
Negative: -1 x -21018415-5 x -4203683-11 x -1910765-55 x -382153-401 x -52415-953 x -22055-2005 x -10483-4411 x -4765


How do I find the factor combinations of the number 21,018,415?

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 21,018,415, 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 21,018,415
-1 -21,018,415

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 21,018,415.

Example:
1 x 21,018,415 = 21,018,415
and
-1 x -21,018,415 = 21,018,415
Notice both answers equal 21,018,415

With that explanation out of the way, let's continue. Next, we take the number 21,018,415 and divide it by 2:

21,018,415 ÷ 2 = 10,509,207.5

If the quotient is a whole number, then 2 and 10,509,207.5 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 21,018,415
-1 -21,018,415

Now, we try dividing 21,018,415 by 3:

21,018,415 ÷ 3 = 7,006,138.3333

If the quotient is a whole number, then 3 and 7,006,138.3333 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 21,018,415
-1 -21,018,415

Let's try dividing by 4:

21,018,415 ÷ 4 = 5,254,603.75

If the quotient is a whole number, then 4 and 5,254,603.75 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 21,018,415
-1 21,018,415
Keep dividing by the next highest number until you cannot divide anymore.

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

1511554019532,0054,4114,76510,48322,05552,415382,1531,910,7654,203,68321,018,415
-1-5-11-55-401-953-2,005-4,411-4,765-10,483-22,055-52,415-382,153-1,910,765-4,203,683-21,018,415

More Examples

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