Q: What are the factor combinations of the number 134,915?

 A:
Positive:   1 x 1349155 x 2698311 x 1226555 x 2453121 x 1115223 x 605
Negative: -1 x -134915-5 x -26983-11 x -12265-55 x -2453-121 x -1115-223 x -605


How do I find the factor combinations of the number 134,915?

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 134,915, 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.

1 134,915
-1 -134,915

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 134,915.

Example:
1 x 134,915 = 134,915
and
-1 x -134,915 = 134,915
Notice both answers equal 134,915

With that explanation out of the way, let's continue. Next, we take the number 134,915 and divide it by 2:

134,915 ÷ 2 = 67,457.5

If the quotient is a whole number, then 2 and 67,457.5 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:

1 134,915
-1 -134,915

Now, we try dividing 134,915 by 3:

134,915 ÷ 3 = 44,971.6667

If the quotient is a whole number, then 3 and 44,971.6667 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:

1 134,915
-1 -134,915

Let's try dividing by 4:

134,915 ÷ 4 = 33,728.75

If the quotient is a whole number, then 4 and 33,728.75 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:

1 134,915
-1 134,915
Keep dividing by the next highest number until you cannot divide anymore.

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

1511551212236051,1152,45312,26526,983134,915
-1-5-11-55-121-223-605-1,115-2,453-12,265-26,983-134,915

More Examples

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