Q: What are the factor combinations of the number 27,209,345?

 A:
Positive:   1 x 272093455 x 544186923 x 1183015115 x 236603223 x 1220151061 x 256451115 x 244035129 x 5305
Negative: -1 x -27209345-5 x -5441869-23 x -1183015-115 x -236603-223 x -122015-1061 x -25645-1115 x -24403-5129 x -5305


How do I find the factor combinations of the number 27,209,345?

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 27,209,345, 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 27,209,345
-1 -27,209,345

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 27,209,345.

Example:
1 x 27,209,345 = 27,209,345
and
-1 x -27,209,345 = 27,209,345
Notice both answers equal 27,209,345

With that explanation out of the way, let's continue. Next, we take the number 27,209,345 and divide it by 2:

27,209,345 ÷ 2 = 13,604,672.5

If the quotient is a whole number, then 2 and 13,604,672.5 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 27,209,345
-1 -27,209,345

Now, we try dividing 27,209,345 by 3:

27,209,345 ÷ 3 = 9,069,781.6667

If the quotient is a whole number, then 3 and 9,069,781.6667 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 27,209,345
-1 -27,209,345

Let's try dividing by 4:

27,209,345 ÷ 4 = 6,802,336.25

If the quotient is a whole number, then 4 and 6,802,336.25 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 27,209,345
-1 27,209,345
Keep dividing by the next highest number until you cannot divide anymore.

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

15231152231,0611,1155,1295,30524,40325,645122,015236,6031,183,0155,441,86927,209,345
-1-5-23-115-223-1,061-1,115-5,129-5,305-24,403-25,645-122,015-236,603-1,183,015-5,441,869-27,209,345

More Examples

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