Q: What are the factor combinations of the number 10,450,349?

 A:
Positive:   1 x 104503497 x 149290713 x 80387323 x 45436391 x 114839161 x 64909299 x 349512093 x 4993
Negative: -1 x -10450349-7 x -1492907-13 x -803873-23 x -454363-91 x -114839-161 x -64909-299 x -34951-2093 x -4993


How do I find the factor combinations of the number 10,450,349?

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 10,450,349, 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 10,450,349
-1 -10,450,349

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 10,450,349.

Example:
1 x 10,450,349 = 10,450,349
and
-1 x -10,450,349 = 10,450,349
Notice both answers equal 10,450,349

With that explanation out of the way, let's continue. Next, we take the number 10,450,349 and divide it by 2:

10,450,349 ÷ 2 = 5,225,174.5

If the quotient is a whole number, then 2 and 5,225,174.5 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 10,450,349
-1 -10,450,349

Now, we try dividing 10,450,349 by 3:

10,450,349 ÷ 3 = 3,483,449.6667

If the quotient is a whole number, then 3 and 3,483,449.6667 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 10,450,349
-1 -10,450,349

Let's try dividing by 4:

10,450,349 ÷ 4 = 2,612,587.25

If the quotient is a whole number, then 4 and 2,612,587.25 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 10,450,349
-1 10,450,349
Keep dividing by the next highest number until you cannot divide anymore.

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

171323911612992,0934,99334,95164,909114,839454,363803,8731,492,90710,450,349
-1-7-13-23-91-161-299-2,093-4,993-34,951-64,909-114,839-454,363-803,873-1,492,907-10,450,349

More Examples

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