Q: What are the factor combinations of the number 27,408,672?

 A:
Positive:   1 x 274086722 x 137043363 x 91362244 x 68521686 x 45681128 x 34260849 x 304540812 x 228405616 x 171304218 x 152270424 x 114202827 x 101513632 x 85652136 x 76135248 x 57101454 x 50756872 x 38067696 x 285507108 x 253784144 x 190338216 x 126892288 x 95169432 x 63446864 x 31723
Negative: -1 x -27408672-2 x -13704336-3 x -9136224-4 x -6852168-6 x -4568112-8 x -3426084-9 x -3045408-12 x -2284056-16 x -1713042-18 x -1522704-24 x -1142028-27 x -1015136-32 x -856521-36 x -761352-48 x -571014-54 x -507568-72 x -380676-96 x -285507-108 x -253784-144 x -190338-216 x -126892-288 x -95169-432 x -63446-864 x -31723


How do I find the factor combinations of the number 27,408,672?

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 27,408,672, 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 27,408,672
-1 -27,408,672

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 27,408,672.

Example:
1 x 27,408,672 = 27,408,672
and
-1 x -27,408,672 = 27,408,672
Notice both answers equal 27,408,672

With that explanation out of the way, let's continue. Next, we take the number 27,408,672 and divide it by 2:

27,408,672 ÷ 2 = 13,704,336

If the quotient is a whole number, then 2 and 13,704,336 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 13,704,336 27,408,672
-1 -2 -13,704,336 -27,408,672

Now, we try dividing 27,408,672 by 3:

27,408,672 ÷ 3 = 9,136,224

If the quotient is a whole number, then 3 and 9,136,224 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 9,136,224 13,704,336 27,408,672
-1 -2 -3 -9,136,224 -13,704,336 -27,408,672

Let's try dividing by 4:

27,408,672 ÷ 4 = 6,852,168

If the quotient is a whole number, then 4 and 6,852,168 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 6,852,168 9,136,224 13,704,336 27,408,672
-1 -2 -3 -4 -6,852,168 -9,136,224 -13,704,336 27,408,672
Keep dividing by the next highest number until you cannot divide anymore.

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

1234689121618242732364854729610814421628843286431,72363,44695,169126,892190,338253,784285,507380,676507,568571,014761,352856,5211,015,1361,142,0281,522,7041,713,0422,284,0563,045,4083,426,0844,568,1126,852,1689,136,22413,704,33627,408,672
-1-2-3-4-6-8-9-12-16-18-24-27-32-36-48-54-72-96-108-144-216-288-432-864-31,723-63,446-95,169-126,892-190,338-253,784-285,507-380,676-507,568-571,014-761,352-856,521-1,015,136-1,142,028-1,522,704-1,713,042-2,284,056-3,045,408-3,426,084-4,568,112-6,852,168-9,136,224-13,704,336-27,408,672

More Examples

Here are some more numbers to try:

27,408,67027,408,67127,408,67327,408,674
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