Q: What are the factor combinations of the number 137,777?

 A:
Positive:   1 x 137777
Negative: -1 x -137777


How do I find the factor combinations of the number 137,777?

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 137,777, 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.

1 137,777
-1 -137,777

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 137,777.

Example:
1 x 137,777 = 137,777
and
-1 x -137,777 = 137,777
Notice both answers equal 137,777

With that explanation out of the way, let's continue. Next, we take the number 137,777 and divide it by 2:

137,777 ÷ 2 = 68,888.5

If the quotient is a whole number, then 2 and 68,888.5 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:

1 137,777
-1 -137,777

Now, we try dividing 137,777 by 3:

137,777 ÷ 3 = 45,925.6667

If the quotient is a whole number, then 3 and 45,925.6667 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:

1 137,777
-1 -137,777

Let's try dividing by 4:

137,777 ÷ 4 = 34,444.25

If the quotient is a whole number, then 4 and 34,444.25 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:

1 137,777
-1 137,777
Keep dividing by the next highest number until you cannot divide anymore.

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

1137,777
-1-137,777

More Examples

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