Q: What are the factor combinations of the number 210,143,125?

 A:
Positive:   1 x 2101431255 x 4202862525 x 8405725101 x 2080625125 x 1681145505 x 416125625 x 3362292525 x 832253329 x 6312512625 x 16645
Negative: -1 x -210143125-5 x -42028625-25 x -8405725-101 x -2080625-125 x -1681145-505 x -416125-625 x -336229-2525 x -83225-3329 x -63125-12625 x -16645


How do I find the factor combinations of the number 210,143,125?

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 210,143,125, 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.

1 210,143,125
-1 -210,143,125

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 210,143,125.

Example:
1 x 210,143,125 = 210,143,125
and
-1 x -210,143,125 = 210,143,125
Notice both answers equal 210,143,125

With that explanation out of the way, let's continue. Next, we take the number 210,143,125 and divide it by 2:

210,143,125 ÷ 2 = 105,071,562.5

If the quotient is a whole number, then 2 and 105,071,562.5 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:

1 210,143,125
-1 -210,143,125

Now, we try dividing 210,143,125 by 3:

210,143,125 ÷ 3 = 70,047,708.3333

If the quotient is a whole number, then 3 and 70,047,708.3333 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:

1 210,143,125
-1 -210,143,125

Let's try dividing by 4:

210,143,125 ÷ 4 = 52,535,781.25

If the quotient is a whole number, then 4 and 52,535,781.25 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:

1 210,143,125
-1 210,143,125
Keep dividing by the next highest number until you cannot divide anymore.

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

15251011255056252,5253,32912,62516,64563,12583,225336,229416,1251,681,1452,080,6258,405,72542,028,625210,143,125
-1-5-25-101-125-505-625-2,525-3,329-12,625-16,645-63,125-83,225-336,229-416,125-1,681,145-2,080,625-8,405,725-42,028,625-210,143,125

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