Q: What are the factor combinations of the number 24,105,301?

 A:
Positive:   1 x 2410530111 x 219139153 x 454817173 x 139337239 x 100859583 x 413471903 x 126672629 x 9169
Negative: -1 x -24105301-11 x -2191391-53 x -454817-173 x -139337-239 x -100859-583 x -41347-1903 x -12667-2629 x -9169


How do I find the factor combinations of the number 24,105,301?

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 24,105,301, 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 24,105,301
-1 -24,105,301

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 24,105,301.

Example:
1 x 24,105,301 = 24,105,301
and
-1 x -24,105,301 = 24,105,301
Notice both answers equal 24,105,301

With that explanation out of the way, let's continue. Next, we take the number 24,105,301 and divide it by 2:

24,105,301 ÷ 2 = 12,052,650.5

If the quotient is a whole number, then 2 and 12,052,650.5 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 24,105,301
-1 -24,105,301

Now, we try dividing 24,105,301 by 3:

24,105,301 ÷ 3 = 8,035,100.3333

If the quotient is a whole number, then 3 and 8,035,100.3333 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 24,105,301
-1 -24,105,301

Let's try dividing by 4:

24,105,301 ÷ 4 = 6,026,325.25

If the quotient is a whole number, then 4 and 6,026,325.25 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 24,105,301
-1 24,105,301
Keep dividing by the next highest number until you cannot divide anymore.

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

111531732395831,9032,6299,16912,66741,347100,859139,337454,8172,191,39124,105,301
-1-11-53-173-239-583-1,903-2,629-9,169-12,667-41,347-100,859-139,337-454,817-2,191,391-24,105,301

More Examples

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