Q: What are the factor combinations of the number 21,240,415?

 A:
Positive:   1 x 212404155 x 42480837 x 303434535 x 606869151 x 140665755 x 281331057 x 200954019 x 5285
Negative: -1 x -21240415-5 x -4248083-7 x -3034345-35 x -606869-151 x -140665-755 x -28133-1057 x -20095-4019 x -5285


How do I find the factor combinations of the number 21,240,415?

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 21,240,415, 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 21,240,415
-1 -21,240,415

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 21,240,415.

Example:
1 x 21,240,415 = 21,240,415
and
-1 x -21,240,415 = 21,240,415
Notice both answers equal 21,240,415

With that explanation out of the way, let's continue. Next, we take the number 21,240,415 and divide it by 2:

21,240,415 ÷ 2 = 10,620,207.5

If the quotient is a whole number, then 2 and 10,620,207.5 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 21,240,415
-1 -21,240,415

Now, we try dividing 21,240,415 by 3:

21,240,415 ÷ 3 = 7,080,138.3333

If the quotient is a whole number, then 3 and 7,080,138.3333 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 21,240,415
-1 -21,240,415

Let's try dividing by 4:

21,240,415 ÷ 4 = 5,310,103.75

If the quotient is a whole number, then 4 and 5,310,103.75 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 21,240,415
-1 21,240,415
Keep dividing by the next highest number until you cannot divide anymore.

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

157351517551,0574,0195,28520,09528,133140,665606,8693,034,3454,248,08321,240,415
-1-5-7-35-151-755-1,057-4,019-5,285-20,095-28,133-140,665-606,869-3,034,345-4,248,083-21,240,415

More Examples

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