Q: What are the factor combinations of the number 1,024,309?

 A:
Positive:   1 x 102430911 x 9311913 x 7879319 x 5391129 x 35321143 x 7163169 x 6061209 x 4901247 x 4147319 x 3211377 x 2717551 x 1859
Negative: -1 x -1024309-11 x -93119-13 x -78793-19 x -53911-29 x -35321-143 x -7163-169 x -6061-209 x -4901-247 x -4147-319 x -3211-377 x -2717-551 x -1859


How do I find the factor combinations of the number 1,024,309?

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 1,024,309, 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 1,024,309
-1 -1,024,309

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 1,024,309.

Example:
1 x 1,024,309 = 1,024,309
and
-1 x -1,024,309 = 1,024,309
Notice both answers equal 1,024,309

With that explanation out of the way, let's continue. Next, we take the number 1,024,309 and divide it by 2:

1,024,309 ÷ 2 = 512,154.5

If the quotient is a whole number, then 2 and 512,154.5 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 1,024,309
-1 -1,024,309

Now, we try dividing 1,024,309 by 3:

1,024,309 ÷ 3 = 341,436.3333

If the quotient is a whole number, then 3 and 341,436.3333 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 1,024,309
-1 -1,024,309

Let's try dividing by 4:

1,024,309 ÷ 4 = 256,077.25

If the quotient is a whole number, then 4 and 256,077.25 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 1,024,309
-1 1,024,309
Keep dividing by the next highest number until you cannot divide anymore.

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

1111319291431692092473193775511,8592,7173,2114,1474,9016,0617,16335,32153,91178,79393,1191,024,309
-1-11-13-19-29-143-169-209-247-319-377-551-1,859-2,717-3,211-4,147-4,901-6,061-7,163-35,321-53,911-78,793-93,119-1,024,309

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