Q: What are the factor combinations of the number 210,900?

 A:
Positive:   1 x 2109002 x 1054503 x 703004 x 527255 x 421806 x 3515010 x 2109012 x 1757515 x 1406019 x 1110020 x 1054525 x 843630 x 703037 x 570038 x 555050 x 421857 x 370060 x 351574 x 285075 x 281276 x 277595 x 2220100 x 2109111 x 1900114 x 1850148 x 1425150 x 1406185 x 1140190 x 1110222 x 950228 x 925285 x 740300 x 703370 x 570380 x 555444 x 475
Negative: -1 x -210900-2 x -105450-3 x -70300-4 x -52725-5 x -42180-6 x -35150-10 x -21090-12 x -17575-15 x -14060-19 x -11100-20 x -10545-25 x -8436-30 x -7030-37 x -5700-38 x -5550-50 x -4218-57 x -3700-60 x -3515-74 x -2850-75 x -2812-76 x -2775-95 x -2220-100 x -2109-111 x -1900-114 x -1850-148 x -1425-150 x -1406-185 x -1140-190 x -1110-222 x -950-228 x -925-285 x -740-300 x -703-370 x -570-380 x -555-444 x -475


How do I find the factor combinations of the number 210,900?

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 210,900, 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.

1 210,900
-1 -210,900

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 210,900.

Example:
1 x 210,900 = 210,900
and
-1 x -210,900 = 210,900
Notice both answers equal 210,900

With that explanation out of the way, let's continue. Next, we take the number 210,900 and divide it by 2:

210,900 ÷ 2 = 105,450

If the quotient is a whole number, then 2 and 105,450 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 105,450 210,900
-1 -2 -105,450 -210,900

Now, we try dividing 210,900 by 3:

210,900 ÷ 3 = 70,300

If the quotient is a whole number, then 3 and 70,300 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 70,300 105,450 210,900
-1 -2 -3 -70,300 -105,450 -210,900

Let's try dividing by 4:

210,900 ÷ 4 = 52,725

If the quotient is a whole number, then 4 and 52,725 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 52,725 70,300 105,450 210,900
-1 -2 -3 -4 -52,725 -70,300 -105,450 210,900
Keep dividing by the next highest number until you cannot divide anymore.

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

123456101215192025303738505760747576951001111141481501851902222282853003703804444755555707037409259501,1101,1401,4061,4251,8501,9002,1092,2202,7752,8122,8503,5153,7004,2185,5505,7007,0308,43610,54511,10014,06017,57521,09035,15042,18052,72570,300105,450210,900
-1-2-3-4-5-6-10-12-15-19-20-25-30-37-38-50-57-60-74-75-76-95-100-111-114-148-150-185-190-222-228-285-300-370-380-444-475-555-570-703-740-925-950-1,110-1,140-1,406-1,425-1,850-1,900-2,109-2,220-2,775-2,812-2,850-3,515-3,700-4,218-5,550-5,700-7,030-8,436-10,545-11,100-14,060-17,575-21,090-35,150-42,180-52,725-70,300-105,450-210,900

More Examples

Here are some more numbers to try:

210,898210,899210,901210,902
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