Q: What are the factor combinations of the number 421,800?

 A:
Positive:   1 x 4218002 x 2109003 x 1406004 x 1054505 x 843606 x 703008 x 5272510 x 4218012 x 3515015 x 2812019 x 2220020 x 2109024 x 1757525 x 1687230 x 1406037 x 1140038 x 1110040 x 1054550 x 843657 x 740060 x 703074 x 570075 x 562476 x 555095 x 4440100 x 4218111 x 3800114 x 3700120 x 3515148 x 2850150 x 2812152 x 2775185 x 2280190 x 2220200 x 2109222 x 1900228 x 1850285 x 1480296 x 1425300 x 1406370 x 1140380 x 1110444 x 950456 x 925475 x 888555 x 760570 x 740600 x 703
Negative: -1 x -421800-2 x -210900-3 x -140600-4 x -105450-5 x -84360-6 x -70300-8 x -52725-10 x -42180-12 x -35150-15 x -28120-19 x -22200-20 x -21090-24 x -17575-25 x -16872-30 x -14060-37 x -11400-38 x -11100-40 x -10545-50 x -8436-57 x -7400-60 x -7030-74 x -5700-75 x -5624-76 x -5550-95 x -4440-100 x -4218-111 x -3800-114 x -3700-120 x -3515-148 x -2850-150 x -2812-152 x -2775-185 x -2280-190 x -2220-200 x -2109-222 x -1900-228 x -1850-285 x -1480-296 x -1425-300 x -1406-370 x -1140-380 x -1110-444 x -950-456 x -925-475 x -888-555 x -760-570 x -740-600 x -703


How do I find the factor combinations of the number 421,800?

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 421,800, 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.

1 421,800
-1 -421,800

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 421,800.

Example:
1 x 421,800 = 421,800
and
-1 x -421,800 = 421,800
Notice both answers equal 421,800

With that explanation out of the way, let's continue. Next, we take the number 421,800 and divide it by 2:

421,800 ÷ 2 = 210,900

If the quotient is a whole number, then 2 and 210,900 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 2 210,900 421,800
-1 -2 -210,900 -421,800

Now, we try dividing 421,800 by 3:

421,800 ÷ 3 = 140,600

If the quotient is a whole number, then 3 and 140,600 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 3 140,600 210,900 421,800
-1 -2 -3 -140,600 -210,900 -421,800

Let's try dividing by 4:

421,800 ÷ 4 = 105,450

If the quotient is a whole number, then 4 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 3 4 105,450 140,600 210,900 421,800
-1 -2 -3 -4 -105,450 -140,600 -210,900 421,800
Keep dividing by the next highest number until you cannot divide anymore.

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

12345681012151920242530373840505760747576951001111141201481501521851902002222282852963003703804444564755555706007037407608889259501,1101,1401,4061,4251,4801,8501,9002,1092,2202,2802,7752,8122,8503,5153,7003,8004,2184,4405,5505,6245,7007,0307,4008,43610,54511,10011,40014,06016,87217,57521,09022,20028,12035,15042,18052,72570,30084,360105,450140,600210,900421,800
-1-2-3-4-5-6-8-10-12-15-19-20-24-25-30-37-38-40-50-57-60-74-75-76-95-100-111-114-120-148-150-152-185-190-200-222-228-285-296-300-370-380-444-456-475-555-570-600-703-740-760-888-925-950-1,110-1,140-1,406-1,425-1,480-1,850-1,900-2,109-2,220-2,280-2,775-2,812-2,850-3,515-3,700-3,800-4,218-4,440-5,550-5,624-5,700-7,030-7,400-8,436-10,545-11,100-11,400-14,060-16,872-17,575-21,090-22,200-28,120-35,150-42,180-52,725-70,300-84,360-105,450-140,600-210,900-421,800

More Examples

Here are some more numbers to try:

421,798421,799421,801421,802
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