Q: What are the factor combinations of the number 4,201,200?

 A:
Positive:   1 x 42012002 x 21006003 x 14004004 x 10503005 x 8402406 x 7002008 x 5251509 x 46680010 x 42012012 x 35010015 x 28008016 x 26257518 x 23340020 x 21006024 x 17505025 x 16804827 x 15560030 x 14004036 x 11670040 x 10503045 x 9336048 x 8752550 x 8402454 x 7780060 x 7002072 x 5835075 x 5601680 x 5251590 x 46680100 x 42012108 x 38900120 x 35010135 x 31120144 x 29175150 x 28008180 x 23340200 x 21006216 x 19450225 x 18672240 x 17505270 x 15560300 x 14004360 x 11670389 x 10800400 x 10503432 x 9725450 x 9336540 x 7780600 x 7002675 x 6224720 x 5835778 x 5400900 x 46681080 x 38901167 x 36001200 x 35011350 x 31121556 x 27001800 x 23341945 x 2160
Negative: -1 x -4201200-2 x -2100600-3 x -1400400-4 x -1050300-5 x -840240-6 x -700200-8 x -525150-9 x -466800-10 x -420120-12 x -350100-15 x -280080-16 x -262575-18 x -233400-20 x -210060-24 x -175050-25 x -168048-27 x -155600-30 x -140040-36 x -116700-40 x -105030-45 x -93360-48 x -87525-50 x -84024-54 x -77800-60 x -70020-72 x -58350-75 x -56016-80 x -52515-90 x -46680-100 x -42012-108 x -38900-120 x -35010-135 x -31120-144 x -29175-150 x -28008-180 x -23340-200 x -21006-216 x -19450-225 x -18672-240 x -17505-270 x -15560-300 x -14004-360 x -11670-389 x -10800-400 x -10503-432 x -9725-450 x -9336-540 x -7780-600 x -7002-675 x -6224-720 x -5835-778 x -5400-900 x -4668-1080 x -3890-1167 x -3600-1200 x -3501-1350 x -3112-1556 x -2700-1800 x -2334-1945 x -2160


How do I find the factor combinations of the number 4,201,200?

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 4,201,200, 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 4,201,200
-1 -4,201,200

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 4,201,200.

Example:
1 x 4,201,200 = 4,201,200
and
-1 x -4,201,200 = 4,201,200
Notice both answers equal 4,201,200

With that explanation out of the way, let's continue. Next, we take the number 4,201,200 and divide it by 2:

4,201,200 ÷ 2 = 2,100,600

If the quotient is a whole number, then 2 and 2,100,600 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 2,100,600 4,201,200
-1 -2 -2,100,600 -4,201,200

Now, we try dividing 4,201,200 by 3:

4,201,200 ÷ 3 = 1,400,400

If the quotient is a whole number, then 3 and 1,400,400 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 1,400,400 2,100,600 4,201,200
-1 -2 -3 -1,400,400 -2,100,600 -4,201,200

Let's try dividing by 4:

4,201,200 ÷ 4 = 1,050,300

If the quotient is a whole number, then 4 and 1,050,300 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 4 1,050,300 1,400,400 2,100,600 4,201,200
-1 -2 -3 -4 -1,050,300 -1,400,400 -2,100,600 4,201,200
Keep dividing by the next highest number until you cannot divide anymore.

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

123456891012151618202425273036404548505460727580901001081201351441501802002162252402703003603894004324505406006757207789001,0801,1671,2001,3501,5561,8001,9452,1602,3342,7003,1123,5013,6003,8904,6685,4005,8356,2247,0027,7809,3369,72510,50310,80011,67014,00415,56017,50518,67219,45021,00623,34028,00829,17531,12035,01038,90042,01246,68052,51556,01658,35070,02077,80084,02487,52593,360105,030116,700140,040155,600168,048175,050210,060233,400262,575280,080350,100420,120466,800525,150700,200840,2401,050,3001,400,4002,100,6004,201,200
-1-2-3-4-5-6-8-9-10-12-15-16-18-20-24-25-27-30-36-40-45-48-50-54-60-72-75-80-90-100-108-120-135-144-150-180-200-216-225-240-270-300-360-389-400-432-450-540-600-675-720-778-900-1,080-1,167-1,200-1,350-1,556-1,800-1,945-2,160-2,334-2,700-3,112-3,501-3,600-3,890-4,668-5,400-5,835-6,224-7,002-7,780-9,336-9,725-10,503-10,800-11,670-14,004-15,560-17,505-18,672-19,450-21,006-23,340-28,008-29,175-31,120-35,010-38,900-42,012-46,680-52,515-56,016-58,350-70,020-77,800-84,024-87,525-93,360-105,030-116,700-140,040-155,600-168,048-175,050-210,060-233,400-262,575-280,080-350,100-420,120-466,800-525,150-700,200-840,240-1,050,300-1,400,400-2,100,600-4,201,200

More Examples

Here are some more numbers to try:

4,201,1984,201,1994,201,2014,201,202
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