Q: What are the factor combinations of the number 14,402,125?

 A:
Positive:   1 x 144021255 x 288042525 x 57608529 x 496625125 x 115217137 x 105125145 x 99325685 x 21025725 x 19865841 x 171253425 x 42053625 x 3973
Negative: -1 x -14402125-5 x -2880425-25 x -576085-29 x -496625-125 x -115217-137 x -105125-145 x -99325-685 x -21025-725 x -19865-841 x -17125-3425 x -4205-3625 x -3973


How do I find the factor combinations of the number 14,402,125?

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 14,402,125, 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 14,402,125
-1 -14,402,125

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 14,402,125.

Example:
1 x 14,402,125 = 14,402,125
and
-1 x -14,402,125 = 14,402,125
Notice both answers equal 14,402,125

With that explanation out of the way, let's continue. Next, we take the number 14,402,125 and divide it by 2:

14,402,125 ÷ 2 = 7,201,062.5

If the quotient is a whole number, then 2 and 7,201,062.5 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 14,402,125
-1 -14,402,125

Now, we try dividing 14,402,125 by 3:

14,402,125 ÷ 3 = 4,800,708.3333

If the quotient is a whole number, then 3 and 4,800,708.3333 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 14,402,125
-1 -14,402,125

Let's try dividing by 4:

14,402,125 ÷ 4 = 3,600,531.25

If the quotient is a whole number, then 4 and 3,600,531.25 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 14,402,125
-1 14,402,125
Keep dividing by the next highest number until you cannot divide anymore.

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

1525291251371456857258413,4253,6253,9734,20517,12519,86521,02599,325105,125115,217496,625576,0852,880,42514,402,125
-1-5-25-29-125-137-145-685-725-841-3,425-3,625-3,973-4,205-17,125-19,865-21,025-99,325-105,125-115,217-496,625-576,085-2,880,425-14,402,125

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