Q: What are the factor combinations of the number 21,070,021?

 A:
Positive:   1 x 210700217 x 301000317 x 123941359 x 357119119 x 177059413 x 510171003 x 210073001 x 7021
Negative: -1 x -21070021-7 x -3010003-17 x -1239413-59 x -357119-119 x -177059-413 x -51017-1003 x -21007-3001 x -7021


How do I find the factor combinations of the number 21,070,021?

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 21,070,021, 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 21,070,021
-1 -21,070,021

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 21,070,021.

Example:
1 x 21,070,021 = 21,070,021
and
-1 x -21,070,021 = 21,070,021
Notice both answers equal 21,070,021

With that explanation out of the way, let's continue. Next, we take the number 21,070,021 and divide it by 2:

21,070,021 ÷ 2 = 10,535,010.5

If the quotient is a whole number, then 2 and 10,535,010.5 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 21,070,021
-1 -21,070,021

Now, we try dividing 21,070,021 by 3:

21,070,021 ÷ 3 = 7,023,340.3333

If the quotient is a whole number, then 3 and 7,023,340.3333 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 21,070,021
-1 -21,070,021

Let's try dividing by 4:

21,070,021 ÷ 4 = 5,267,505.25

If the quotient is a whole number, then 4 and 5,267,505.25 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 21,070,021
-1 21,070,021
Keep dividing by the next highest number until you cannot divide anymore.

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

1717591194131,0033,0017,02121,00751,017177,059357,1191,239,4133,010,00321,070,021
-1-7-17-59-119-413-1,003-3,001-7,021-21,007-51,017-177,059-357,119-1,239,413-3,010,003-21,070,021

More Examples

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