Q: What are the factor combinations of the number 132,105,203?

 A:
Positive:   1 x 13210520347 x 281074953 x 2492551181 x 729863293 x 4508712491 x 530338507 x 155299593 x 13771
Negative: -1 x -132105203-47 x -2810749-53 x -2492551-181 x -729863-293 x -450871-2491 x -53033-8507 x -15529-9593 x -13771


How do I find the factor combinations of the number 132,105,203?

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 132,105,203, 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.

1 132,105,203
-1 -132,105,203

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 132,105,203.

Example:
1 x 132,105,203 = 132,105,203
and
-1 x -132,105,203 = 132,105,203
Notice both answers equal 132,105,203

With that explanation out of the way, let's continue. Next, we take the number 132,105,203 and divide it by 2:

132,105,203 ÷ 2 = 66,052,601.5

If the quotient is a whole number, then 2 and 66,052,601.5 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:

1 132,105,203
-1 -132,105,203

Now, we try dividing 132,105,203 by 3:

132,105,203 ÷ 3 = 44,035,067.6667

If the quotient is a whole number, then 3 and 44,035,067.6667 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:

1 132,105,203
-1 -132,105,203

Let's try dividing by 4:

132,105,203 ÷ 4 = 33,026,300.75

If the quotient is a whole number, then 4 and 33,026,300.75 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:

1 132,105,203
-1 132,105,203
Keep dividing by the next highest number until you cannot divide anymore.

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

147531812932,4918,5079,59313,77115,52953,033450,871729,8632,492,5512,810,749132,105,203
-1-47-53-181-293-2,491-8,507-9,593-13,771-15,529-53,033-450,871-729,863-2,492,551-2,810,749-132,105,203

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