Q: What are the factor combinations of the number 21,194,329?

 A:
Positive:   1 x 2119432913 x 163033319 x 111549153 x 399893247 x 85807689 x 307611007 x 210471619 x 13091
Negative: -1 x -21194329-13 x -1630333-19 x -1115491-53 x -399893-247 x -85807-689 x -30761-1007 x -21047-1619 x -13091


How do I find the factor combinations of the number 21,194,329?

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 21,194,329, 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 21,194,329
-1 -21,194,329

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 21,194,329.

Example:
1 x 21,194,329 = 21,194,329
and
-1 x -21,194,329 = 21,194,329
Notice both answers equal 21,194,329

With that explanation out of the way, let's continue. Next, we take the number 21,194,329 and divide it by 2:

21,194,329 ÷ 2 = 10,597,164.5

If the quotient is a whole number, then 2 and 10,597,164.5 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 21,194,329
-1 -21,194,329

Now, we try dividing 21,194,329 by 3:

21,194,329 ÷ 3 = 7,064,776.3333

If the quotient is a whole number, then 3 and 7,064,776.3333 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 21,194,329
-1 -21,194,329

Let's try dividing by 4:

21,194,329 ÷ 4 = 5,298,582.25

If the quotient is a whole number, then 4 and 5,298,582.25 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 21,194,329
-1 21,194,329
Keep dividing by the next highest number until you cannot divide anymore.

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

11319532476891,0071,61913,09121,04730,76185,807399,8931,115,4911,630,33321,194,329
-1-13-19-53-247-689-1,007-1,619-13,091-21,047-30,761-85,807-399,893-1,115,491-1,630,333-21,194,329

More Examples

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