Q: What are the factor combinations of the number 17,238,221?

 A:
Positive:   1 x 172382217 x 246260311 x 156711113 x 132601717 x 101401377 x 22387391 x 189431119 x 144859143 x 120547187 x 92183221 x 780011001 x 172211013 x 170171309 x 131691547 x 111432431 x 7091
Negative: -1 x -17238221-7 x -2462603-11 x -1567111-13 x -1326017-17 x -1014013-77 x -223873-91 x -189431-119 x -144859-143 x -120547-187 x -92183-221 x -78001-1001 x -17221-1013 x -17017-1309 x -13169-1547 x -11143-2431 x -7091


How do I find the factor combinations of the number 17,238,221?

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 17,238,221, 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 17,238,221
-1 -17,238,221

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 17,238,221.

Example:
1 x 17,238,221 = 17,238,221
and
-1 x -17,238,221 = 17,238,221
Notice both answers equal 17,238,221

With that explanation out of the way, let's continue. Next, we take the number 17,238,221 and divide it by 2:

17,238,221 ÷ 2 = 8,619,110.5

If the quotient is a whole number, then 2 and 8,619,110.5 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 17,238,221
-1 -17,238,221

Now, we try dividing 17,238,221 by 3:

17,238,221 ÷ 3 = 5,746,073.6667

If the quotient is a whole number, then 3 and 5,746,073.6667 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 17,238,221
-1 -17,238,221

Let's try dividing by 4:

17,238,221 ÷ 4 = 4,309,555.25

If the quotient is a whole number, then 4 and 4,309,555.25 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 17,238,221
-1 17,238,221
Keep dividing by the next highest number until you cannot divide anymore.

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

1711131777911191431872211,0011,0131,3091,5472,4317,09111,14313,16917,01717,22178,00192,183120,547144,859189,431223,8731,014,0131,326,0171,567,1112,462,60317,238,221
-1-7-11-13-17-77-91-119-143-187-221-1,001-1,013-1,309-1,547-2,431-7,091-11,143-13,169-17,017-17,221-78,001-92,183-120,547-144,859-189,431-223,873-1,014,013-1,326,017-1,567,111-2,462,603-17,238,221

More Examples

Here are some more numbers to try:

17,238,21917,238,22017,238,22217,238,223
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