Q: What are the factor combinations of the number 21,435,271?

 A:
Positive:   1 x 2143527111 x 194866113 x 1648867121 x 177151143 x 1498971573 x 13627
Negative: -1 x -21435271-11 x -1948661-13 x -1648867-121 x -177151-143 x -149897-1573 x -13627


How do I find the factor combinations of the number 21,435,271?

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 21,435,271, 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 21,435,271
-1 -21,435,271

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 21,435,271.

Example:
1 x 21,435,271 = 21,435,271
and
-1 x -21,435,271 = 21,435,271
Notice both answers equal 21,435,271

With that explanation out of the way, let's continue. Next, we take the number 21,435,271 and divide it by 2:

21,435,271 ÷ 2 = 10,717,635.5

If the quotient is a whole number, then 2 and 10,717,635.5 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 21,435,271
-1 -21,435,271

Now, we try dividing 21,435,271 by 3:

21,435,271 ÷ 3 = 7,145,090.3333

If the quotient is a whole number, then 3 and 7,145,090.3333 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 21,435,271
-1 -21,435,271

Let's try dividing by 4:

21,435,271 ÷ 4 = 5,358,817.75

If the quotient is a whole number, then 4 and 5,358,817.75 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 21,435,271
-1 21,435,271
Keep dividing by the next highest number until you cannot divide anymore.

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

111131211431,57313,627149,897177,1511,648,8671,948,66121,435,271
-1-11-13-121-143-1,573-13,627-149,897-177,151-1,648,867-1,948,661-21,435,271

More Examples

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