Q: What are the factor combinations of the number 450,342,319?

 A:
Positive:   1 x 4503423197 x 6433461741 x 10983959287 x 15691371013 x 4445631549 x 2907317091 x 6350910843 x 41533
Negative: -1 x -450342319-7 x -64334617-41 x -10983959-287 x -1569137-1013 x -444563-1549 x -290731-7091 x -63509-10843 x -41533


How do I find the factor combinations of the number 450,342,319?

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 450,342,319, 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.

1 450,342,319
-1 -450,342,319

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 450,342,319.

Example:
1 x 450,342,319 = 450,342,319
and
-1 x -450,342,319 = 450,342,319
Notice both answers equal 450,342,319

With that explanation out of the way, let's continue. Next, we take the number 450,342,319 and divide it by 2:

450,342,319 ÷ 2 = 225,171,159.5

If the quotient is a whole number, then 2 and 225,171,159.5 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:

1 450,342,319
-1 -450,342,319

Now, we try dividing 450,342,319 by 3:

450,342,319 ÷ 3 = 150,114,106.3333

If the quotient is a whole number, then 3 and 150,114,106.3333 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:

1 450,342,319
-1 -450,342,319

Let's try dividing by 4:

450,342,319 ÷ 4 = 112,585,579.75

If the quotient is a whole number, then 4 and 112,585,579.75 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:

1 450,342,319
-1 450,342,319
Keep dividing by the next highest number until you cannot divide anymore.

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

17412871,0131,5497,09110,84341,53363,509290,731444,5631,569,13710,983,95964,334,617450,342,319
-1-7-41-287-1,013-1,549-7,091-10,843-41,533-63,509-290,731-444,563-1,569,137-10,983,959-64,334,617-450,342,319

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