Q: What are the factor combinations of the number 87,406,123?

 A:
Positive:   1 x 874061237 x 1248658967 x 1304569227 x 385049469 x 186367821 x 1064631589 x 550075747 x 15209
Negative: -1 x -87406123-7 x -12486589-67 x -1304569-227 x -385049-469 x -186367-821 x -106463-1589 x -55007-5747 x -15209


How do I find the factor combinations of the number 87,406,123?

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 87,406,123, 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 87,406,123
-1 -87,406,123

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 87,406,123.

Example:
1 x 87,406,123 = 87,406,123
and
-1 x -87,406,123 = 87,406,123
Notice both answers equal 87,406,123

With that explanation out of the way, let's continue. Next, we take the number 87,406,123 and divide it by 2:

87,406,123 ÷ 2 = 43,703,061.5

If the quotient is a whole number, then 2 and 43,703,061.5 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 87,406,123
-1 -87,406,123

Now, we try dividing 87,406,123 by 3:

87,406,123 ÷ 3 = 29,135,374.3333

If the quotient is a whole number, then 3 and 29,135,374.3333 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 87,406,123
-1 -87,406,123

Let's try dividing by 4:

87,406,123 ÷ 4 = 21,851,530.75

If the quotient is a whole number, then 4 and 21,851,530.75 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 87,406,123
-1 87,406,123
Keep dividing by the next highest number until you cannot divide anymore.

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

17672274698211,5895,74715,20955,007106,463186,367385,0491,304,56912,486,58987,406,123
-1-7-67-227-469-821-1,589-5,747-15,209-55,007-106,463-186,367-385,049-1,304,569-12,486,589-87,406,123

More Examples

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