Q: What are the factor combinations of the number 1,653,421?

 A:
Positive:   1 x 16534217 x 23620311 x 15031177 x 21473109 x 15169197 x 8393763 x 21671199 x 1379
Negative: -1 x -1653421-7 x -236203-11 x -150311-77 x -21473-109 x -15169-197 x -8393-763 x -2167-1199 x -1379


How do I find the factor combinations of the number 1,653,421?

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 1,653,421, 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 1,653,421
-1 -1,653,421

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 1,653,421.

Example:
1 x 1,653,421 = 1,653,421
and
-1 x -1,653,421 = 1,653,421
Notice both answers equal 1,653,421

With that explanation out of the way, let's continue. Next, we take the number 1,653,421 and divide it by 2:

1,653,421 ÷ 2 = 826,710.5

If the quotient is a whole number, then 2 and 826,710.5 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 1,653,421
-1 -1,653,421

Now, we try dividing 1,653,421 by 3:

1,653,421 ÷ 3 = 551,140.3333

If the quotient is a whole number, then 3 and 551,140.3333 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 1,653,421
-1 -1,653,421

Let's try dividing by 4:

1,653,421 ÷ 4 = 413,355.25

If the quotient is a whole number, then 4 and 413,355.25 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 1,653,421
-1 1,653,421
Keep dividing by the next highest number until you cannot divide anymore.

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

1711771091977631,1991,3792,1678,39315,16921,473150,311236,2031,653,421
-1-7-11-77-109-197-763-1,199-1,379-2,167-8,393-15,169-21,473-150,311-236,203-1,653,421

More Examples

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