Q: What are the factor combinations of the number 100,301,425?

 A:
Positive:   1 x 1003014255 x 200602857 x 1432877525 x 401205735 x 2865755127 x 789775175 x 573151635 x 157955889 x 1128253175 x 315914445 x 225654513 x 22225
Negative: -1 x -100301425-5 x -20060285-7 x -14328775-25 x -4012057-35 x -2865755-127 x -789775-175 x -573151-635 x -157955-889 x -112825-3175 x -31591-4445 x -22565-4513 x -22225


How do I find the factor combinations of the number 100,301,425?

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 100,301,425, 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.

1 100,301,425
-1 -100,301,425

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 100,301,425.

Example:
1 x 100,301,425 = 100,301,425
and
-1 x -100,301,425 = 100,301,425
Notice both answers equal 100,301,425

With that explanation out of the way, let's continue. Next, we take the number 100,301,425 and divide it by 2:

100,301,425 ÷ 2 = 50,150,712.5

If the quotient is a whole number, then 2 and 50,150,712.5 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:

1 100,301,425
-1 -100,301,425

Now, we try dividing 100,301,425 by 3:

100,301,425 ÷ 3 = 33,433,808.3333

If the quotient is a whole number, then 3 and 33,433,808.3333 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:

1 100,301,425
-1 -100,301,425

Let's try dividing by 4:

100,301,425 ÷ 4 = 25,075,356.25

If the quotient is a whole number, then 4 and 25,075,356.25 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:

1 100,301,425
-1 100,301,425
Keep dividing by the next highest number until you cannot divide anymore.

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

15725351271756358893,1754,4454,51322,22522,56531,591112,825157,955573,151789,7752,865,7554,012,05714,328,77520,060,285100,301,425
-1-5-7-25-35-127-175-635-889-3,175-4,445-4,513-22,225-22,565-31,591-112,825-157,955-573,151-789,775-2,865,755-4,012,057-14,328,775-20,060,285-100,301,425

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