Q: What are the factor combinations of the number 45,110,424?

 A:
Positive:   1 x 451104242 x 225552123 x 150368084 x 112776066 x 75184048 x 563880312 x 375920224 x 1879601
Negative: -1 x -45110424-2 x -22555212-3 x -15036808-4 x -11277606-6 x -7518404-8 x -5638803-12 x -3759202-24 x -1879601


How do I find the factor combinations of the number 45,110,424?

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 45,110,424, 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 45,110,424
-1 -45,110,424

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 45,110,424.

Example:
1 x 45,110,424 = 45,110,424
and
-1 x -45,110,424 = 45,110,424
Notice both answers equal 45,110,424

With that explanation out of the way, let's continue. Next, we take the number 45,110,424 and divide it by 2:

45,110,424 ÷ 2 = 22,555,212

If the quotient is a whole number, then 2 and 22,555,212 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 22,555,212 45,110,424
-1 -2 -22,555,212 -45,110,424

Now, we try dividing 45,110,424 by 3:

45,110,424 ÷ 3 = 15,036,808

If the quotient is a whole number, then 3 and 15,036,808 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 15,036,808 22,555,212 45,110,424
-1 -2 -3 -15,036,808 -22,555,212 -45,110,424

Let's try dividing by 4:

45,110,424 ÷ 4 = 11,277,606

If the quotient is a whole number, then 4 and 11,277,606 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 11,277,606 15,036,808 22,555,212 45,110,424
-1 -2 -3 -4 -11,277,606 -15,036,808 -22,555,212 45,110,424
Keep dividing by the next highest number until you cannot divide anymore.

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

12346812241,879,6013,759,2025,638,8037,518,40411,277,60615,036,80822,555,21245,110,424
-1-2-3-4-6-8-12-24-1,879,601-3,759,202-5,638,803-7,518,404-11,277,606-15,036,808-22,555,212-45,110,424

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