Q: What are the factor combinations of the number 10,421,747?

 A:
Positive:   1 x 104217477 x 148882119 x 548513127 x 82061133 x 78359617 x 16891889 x 117232413 x 4319
Negative: -1 x -10421747-7 x -1488821-19 x -548513-127 x -82061-133 x -78359-617 x -16891-889 x -11723-2413 x -4319


How do I find the factor combinations of the number 10,421,747?

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 10,421,747, 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 10,421,747
-1 -10,421,747

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 10,421,747.

Example:
1 x 10,421,747 = 10,421,747
and
-1 x -10,421,747 = 10,421,747
Notice both answers equal 10,421,747

With that explanation out of the way, let's continue. Next, we take the number 10,421,747 and divide it by 2:

10,421,747 ÷ 2 = 5,210,873.5

If the quotient is a whole number, then 2 and 5,210,873.5 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 10,421,747
-1 -10,421,747

Now, we try dividing 10,421,747 by 3:

10,421,747 ÷ 3 = 3,473,915.6667

If the quotient is a whole number, then 3 and 3,473,915.6667 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 10,421,747
-1 -10,421,747

Let's try dividing by 4:

10,421,747 ÷ 4 = 2,605,436.75

If the quotient is a whole number, then 4 and 2,605,436.75 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 10,421,747
-1 10,421,747
Keep dividing by the next highest number until you cannot divide anymore.

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

17191271336178892,4134,31911,72316,89178,35982,061548,5131,488,82110,421,747
-1-7-19-127-133-617-889-2,413-4,319-11,723-16,891-78,359-82,061-548,513-1,488,821-10,421,747

More Examples

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