Q: What are the factor combinations of the number 17,357,221?

 A:
Positive:   1 x 173572217 x 247960317 x 102101349 x 35422967 x 259063119 x 145859311 x 55811469 x 37009833 x 208371139 x 152392177 x 79733283 x 5287
Negative: -1 x -17357221-7 x -2479603-17 x -1021013-49 x -354229-67 x -259063-119 x -145859-311 x -55811-469 x -37009-833 x -20837-1139 x -15239-2177 x -7973-3283 x -5287


How do I find the factor combinations of the number 17,357,221?

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 17,357,221, 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 17,357,221
-1 -17,357,221

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 17,357,221.

Example:
1 x 17,357,221 = 17,357,221
and
-1 x -17,357,221 = 17,357,221
Notice both answers equal 17,357,221

With that explanation out of the way, let's continue. Next, we take the number 17,357,221 and divide it by 2:

17,357,221 ÷ 2 = 8,678,610.5

If the quotient is a whole number, then 2 and 8,678,610.5 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 17,357,221
-1 -17,357,221

Now, we try dividing 17,357,221 by 3:

17,357,221 ÷ 3 = 5,785,740.3333

If the quotient is a whole number, then 3 and 5,785,740.3333 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 17,357,221
-1 -17,357,221

Let's try dividing by 4:

17,357,221 ÷ 4 = 4,339,305.25

If the quotient is a whole number, then 4 and 4,339,305.25 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 17,357,221
-1 17,357,221
Keep dividing by the next highest number until you cannot divide anymore.

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

171749671193114698331,1392,1773,2835,2877,97315,23920,83737,00955,811145,859259,063354,2291,021,0132,479,60317,357,221
-1-7-17-49-67-119-311-469-833-1,139-2,177-3,283-5,287-7,973-15,239-20,837-37,009-55,811-145,859-259,063-354,229-1,021,013-2,479,603-17,357,221

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