Q: What are the factor combinations of the number 21,535,429?

 A:
Positive:   1 x 2153542923 x 93632329 x 74260183 x 259463389 x 55361667 x 322871909 x 112812407 x 8947
Negative: -1 x -21535429-23 x -936323-29 x -742601-83 x -259463-389 x -55361-667 x -32287-1909 x -11281-2407 x -8947


How do I find the factor combinations of the number 21,535,429?

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 21,535,429, 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 21,535,429
-1 -21,535,429

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 21,535,429.

Example:
1 x 21,535,429 = 21,535,429
and
-1 x -21,535,429 = 21,535,429
Notice both answers equal 21,535,429

With that explanation out of the way, let's continue. Next, we take the number 21,535,429 and divide it by 2:

21,535,429 ÷ 2 = 10,767,714.5

If the quotient is a whole number, then 2 and 10,767,714.5 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 21,535,429
-1 -21,535,429

Now, we try dividing 21,535,429 by 3:

21,535,429 ÷ 3 = 7,178,476.3333

If the quotient is a whole number, then 3 and 7,178,476.3333 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 21,535,429
-1 -21,535,429

Let's try dividing by 4:

21,535,429 ÷ 4 = 5,383,857.25

If the quotient is a whole number, then 4 and 5,383,857.25 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 21,535,429
-1 21,535,429
Keep dividing by the next highest number until you cannot divide anymore.

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

12329833896671,9092,4078,94711,28132,28755,361259,463742,601936,32321,535,429
-1-23-29-83-389-667-1,909-2,407-8,947-11,281-32,287-55,361-259,463-742,601-936,323-21,535,429

More Examples

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