Q: What are the factor combinations of the number 210,402,101?

 A:
Positive:   1 x 2104021017 x 3005744313 x 1618477791 x 23121111019 x 2064792269 x 927297133 x 2949713247 x 15883
Negative: -1 x -210402101-7 x -30057443-13 x -16184777-91 x -2312111-1019 x -206479-2269 x -92729-7133 x -29497-13247 x -15883


How do I find the factor combinations of the number 210,402,101?

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 210,402,101, 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.

1 210,402,101
-1 -210,402,101

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 210,402,101.

Example:
1 x 210,402,101 = 210,402,101
and
-1 x -210,402,101 = 210,402,101
Notice both answers equal 210,402,101

With that explanation out of the way, let's continue. Next, we take the number 210,402,101 and divide it by 2:

210,402,101 ÷ 2 = 105,201,050.5

If the quotient is a whole number, then 2 and 105,201,050.5 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:

1 210,402,101
-1 -210,402,101

Now, we try dividing 210,402,101 by 3:

210,402,101 ÷ 3 = 70,134,033.6667

If the quotient is a whole number, then 3 and 70,134,033.6667 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:

1 210,402,101
-1 -210,402,101

Let's try dividing by 4:

210,402,101 ÷ 4 = 52,600,525.25

If the quotient is a whole number, then 4 and 52,600,525.25 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:

1 210,402,101
-1 210,402,101
Keep dividing by the next highest number until you cannot divide anymore.

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

1713911,0192,2697,13313,24715,88329,49792,729206,4792,312,11116,184,77730,057,443210,402,101
-1-7-13-91-1,019-2,269-7,133-13,247-15,883-29,497-92,729-206,479-2,312,111-16,184,777-30,057,443-210,402,101

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