Q: What are the factor combinations of the number 3,689,221?

 A:
Positive:   1 x 368922117 x 21701341 x 8998167 x 5506379 x 46699697 x 52931139 x 32391343 x 2747
Negative: -1 x -3689221-17 x -217013-41 x -89981-67 x -55063-79 x -46699-697 x -5293-1139 x -3239-1343 x -2747


How do I find the factor combinations of the number 3,689,221?

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 3,689,221, 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 3,689,221
-1 -3,689,221

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 3,689,221.

Example:
1 x 3,689,221 = 3,689,221
and
-1 x -3,689,221 = 3,689,221
Notice both answers equal 3,689,221

With that explanation out of the way, let's continue. Next, we take the number 3,689,221 and divide it by 2:

3,689,221 ÷ 2 = 1,844,610.5

If the quotient is a whole number, then 2 and 1,844,610.5 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 3,689,221
-1 -3,689,221

Now, we try dividing 3,689,221 by 3:

3,689,221 ÷ 3 = 1,229,740.3333

If the quotient is a whole number, then 3 and 1,229,740.3333 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 3,689,221
-1 -3,689,221

Let's try dividing by 4:

3,689,221 ÷ 4 = 922,305.25

If the quotient is a whole number, then 4 and 922,305.25 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 3,689,221
-1 3,689,221
Keep dividing by the next highest number until you cannot divide anymore.

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

1174167796971,1391,3432,7473,2395,29346,69955,06389,981217,0133,689,221
-1-17-41-67-79-697-1,139-1,343-2,747-3,239-5,293-46,699-55,063-89,981-217,013-3,689,221

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