Q: What are the factor combinations of the number 24,612,419?

 A:
Positive:   1 x 2461241913 x 189326331 x 793949157 x 156767389 x 63271403 x 610732041 x 120594867 x 5057
Negative: -1 x -24612419-13 x -1893263-31 x -793949-157 x -156767-389 x -63271-403 x -61073-2041 x -12059-4867 x -5057


How do I find the factor combinations of the number 24,612,419?

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 24,612,419, 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 24,612,419
-1 -24,612,419

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 24,612,419.

Example:
1 x 24,612,419 = 24,612,419
and
-1 x -24,612,419 = 24,612,419
Notice both answers equal 24,612,419

With that explanation out of the way, let's continue. Next, we take the number 24,612,419 and divide it by 2:

24,612,419 ÷ 2 = 12,306,209.5

If the quotient is a whole number, then 2 and 12,306,209.5 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 24,612,419
-1 -24,612,419

Now, we try dividing 24,612,419 by 3:

24,612,419 ÷ 3 = 8,204,139.6667

If the quotient is a whole number, then 3 and 8,204,139.6667 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 24,612,419
-1 -24,612,419

Let's try dividing by 4:

24,612,419 ÷ 4 = 6,153,104.75

If the quotient is a whole number, then 4 and 6,153,104.75 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 24,612,419
-1 24,612,419
Keep dividing by the next highest number until you cannot divide anymore.

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

113311573894032,0414,8675,05712,05961,07363,271156,767793,9491,893,26324,612,419
-1-13-31-157-389-403-2,041-4,867-5,057-12,059-61,073-63,271-156,767-793,949-1,893,263-24,612,419

More Examples

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