Q: What are the factor combinations of the number 100,425,523?

 A:
Positive:   1 x 10042552311 x 912959331 x 323953341 x 2449403121 x 829963341 x 294503451 x 222673653 x 1537911271 x 790133751 x 267734961 x 202437183 x 13981
Negative: -1 x -100425523-11 x -9129593-31 x -3239533-41 x -2449403-121 x -829963-341 x -294503-451 x -222673-653 x -153791-1271 x -79013-3751 x -26773-4961 x -20243-7183 x -13981


How do I find the factor combinations of the number 100,425,523?

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 100,425,523, 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.

1 100,425,523
-1 -100,425,523

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 100,425,523.

Example:
1 x 100,425,523 = 100,425,523
and
-1 x -100,425,523 = 100,425,523
Notice both answers equal 100,425,523

With that explanation out of the way, let's continue. Next, we take the number 100,425,523 and divide it by 2:

100,425,523 ÷ 2 = 50,212,761.5

If the quotient is a whole number, then 2 and 50,212,761.5 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:

1 100,425,523
-1 -100,425,523

Now, we try dividing 100,425,523 by 3:

100,425,523 ÷ 3 = 33,475,174.3333

If the quotient is a whole number, then 3 and 33,475,174.3333 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:

1 100,425,523
-1 -100,425,523

Let's try dividing by 4:

100,425,523 ÷ 4 = 25,106,380.75

If the quotient is a whole number, then 4 and 25,106,380.75 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:

1 100,425,523
-1 100,425,523
Keep dividing by the next highest number until you cannot divide anymore.

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

11131411213414516531,2713,7514,9617,18313,98120,24326,77379,013153,791222,673294,503829,9632,449,4033,239,5339,129,593100,425,523
-1-11-31-41-121-341-451-653-1,271-3,751-4,961-7,183-13,981-20,243-26,773-79,013-153,791-222,673-294,503-829,963-2,449,403-3,239,533-9,129,593-100,425,523

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