Q: What are the factor combinations of the number 110,202,421?

 A:
Positive:   1 x 1102024217 x 1574320343 x 256284749 x 2249029193 x 570997271 x 406651301 x 3661211351 x 815711897 x 580932107 x 523038299 x 132799457 x 11653
Negative: -1 x -110202421-7 x -15743203-43 x -2562847-49 x -2249029-193 x -570997-271 x -406651-301 x -366121-1351 x -81571-1897 x -58093-2107 x -52303-8299 x -13279-9457 x -11653


How do I find the factor combinations of the number 110,202,421?

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 110,202,421, 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.

1 110,202,421
-1 -110,202,421

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 110,202,421.

Example:
1 x 110,202,421 = 110,202,421
and
-1 x -110,202,421 = 110,202,421
Notice both answers equal 110,202,421

With that explanation out of the way, let's continue. Next, we take the number 110,202,421 and divide it by 2:

110,202,421 ÷ 2 = 55,101,210.5

If the quotient is a whole number, then 2 and 55,101,210.5 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:

1 110,202,421
-1 -110,202,421

Now, we try dividing 110,202,421 by 3:

110,202,421 ÷ 3 = 36,734,140.3333

If the quotient is a whole number, then 3 and 36,734,140.3333 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:

1 110,202,421
-1 -110,202,421

Let's try dividing by 4:

110,202,421 ÷ 4 = 27,550,605.25

If the quotient is a whole number, then 4 and 27,550,605.25 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:

1 110,202,421
-1 110,202,421
Keep dividing by the next highest number until you cannot divide anymore.

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

1743491932713011,3511,8972,1078,2999,45711,65313,27952,30358,09381,571366,121406,651570,9972,249,0292,562,84715,743,203110,202,421
-1-7-43-49-193-271-301-1,351-1,897-2,107-8,299-9,457-11,653-13,279-52,303-58,093-81,571-366,121-406,651-570,997-2,249,029-2,562,847-15,743,203-110,202,421

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