Q: What are the factor combinations of the number 21,417,845?

 A:
Positive:   1 x 214178455 x 428356919 x 112725595 x 225451131 x 163495655 x 326991721 x 124452489 x 8605
Negative: -1 x -21417845-5 x -4283569-19 x -1127255-95 x -225451-131 x -163495-655 x -32699-1721 x -12445-2489 x -8605


How do I find the factor combinations of the number 21,417,845?

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 21,417,845, 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 21,417,845
-1 -21,417,845

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 21,417,845.

Example:
1 x 21,417,845 = 21,417,845
and
-1 x -21,417,845 = 21,417,845
Notice both answers equal 21,417,845

With that explanation out of the way, let's continue. Next, we take the number 21,417,845 and divide it by 2:

21,417,845 ÷ 2 = 10,708,922.5

If the quotient is a whole number, then 2 and 10,708,922.5 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 21,417,845
-1 -21,417,845

Now, we try dividing 21,417,845 by 3:

21,417,845 ÷ 3 = 7,139,281.6667

If the quotient is a whole number, then 3 and 7,139,281.6667 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 21,417,845
-1 -21,417,845

Let's try dividing by 4:

21,417,845 ÷ 4 = 5,354,461.25

If the quotient is a whole number, then 4 and 5,354,461.25 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 21,417,845
-1 21,417,845
Keep dividing by the next highest number until you cannot divide anymore.

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

1519951316551,7212,4898,60512,44532,699163,495225,4511,127,2554,283,56921,417,845
-1-5-19-95-131-655-1,721-2,489-8,605-12,445-32,699-163,495-225,451-1,127,255-4,283,569-21,417,845

More Examples

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