Q: What are the factor combinations of the number 10,460,723?

 A:
Positive:   1 x 104607237 x 149438913 x 80467191 x 114953139 x 75257827 x 12649973 x 107511807 x 5789
Negative: -1 x -10460723-7 x -1494389-13 x -804671-91 x -114953-139 x -75257-827 x -12649-973 x -10751-1807 x -5789


How do I find the factor combinations of the number 10,460,723?

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 10,460,723, 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 10,460,723
-1 -10,460,723

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 10,460,723.

Example:
1 x 10,460,723 = 10,460,723
and
-1 x -10,460,723 = 10,460,723
Notice both answers equal 10,460,723

With that explanation out of the way, let's continue. Next, we take the number 10,460,723 and divide it by 2:

10,460,723 ÷ 2 = 5,230,361.5

If the quotient is a whole number, then 2 and 5,230,361.5 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 10,460,723
-1 -10,460,723

Now, we try dividing 10,460,723 by 3:

10,460,723 ÷ 3 = 3,486,907.6667

If the quotient is a whole number, then 3 and 3,486,907.6667 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 10,460,723
-1 -10,460,723

Let's try dividing by 4:

10,460,723 ÷ 4 = 2,615,180.75

If the quotient is a whole number, then 4 and 2,615,180.75 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 10,460,723
-1 10,460,723
Keep dividing by the next highest number until you cannot divide anymore.

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

1713911398279731,8075,78910,75112,64975,257114,953804,6711,494,38910,460,723
-1-7-13-91-139-827-973-1,807-5,789-10,751-12,649-75,257-114,953-804,671-1,494,389-10,460,723

More Examples

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