Q: What are the factor combinations of the number 134,646,421?

 A:
Positive:   1 x 1346464217 x 1923520313 x 1035741791 x 1479631479 x 2810993089 x 435893353 x 401576227 x 21623
Negative: -1 x -134646421-7 x -19235203-13 x -10357417-91 x -1479631-479 x -281099-3089 x -43589-3353 x -40157-6227 x -21623


How do I find the factor combinations of the number 134,646,421?

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 134,646,421, 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.

1 134,646,421
-1 -134,646,421

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 134,646,421.

Example:
1 x 134,646,421 = 134,646,421
and
-1 x -134,646,421 = 134,646,421
Notice both answers equal 134,646,421

With that explanation out of the way, let's continue. Next, we take the number 134,646,421 and divide it by 2:

134,646,421 ÷ 2 = 67,323,210.5

If the quotient is a whole number, then 2 and 67,323,210.5 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:

1 134,646,421
-1 -134,646,421

Now, we try dividing 134,646,421 by 3:

134,646,421 ÷ 3 = 44,882,140.3333

If the quotient is a whole number, then 3 and 44,882,140.3333 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:

1 134,646,421
-1 -134,646,421

Let's try dividing by 4:

134,646,421 ÷ 4 = 33,661,605.25

If the quotient is a whole number, then 4 and 33,661,605.25 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:

1 134,646,421
-1 134,646,421
Keep dividing by the next highest number until you cannot divide anymore.

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

1713914793,0893,3536,22721,62340,15743,589281,0991,479,63110,357,41719,235,203134,646,421
-1-7-13-91-479-3,089-3,353-6,227-21,623-40,157-43,589-281,099-1,479,631-10,357,417-19,235,203-134,646,421

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