Q: What are the factor combinations of the number 388,800?

 A:
Positive:   1 x 3888002 x 1944003 x 1296004 x 972005 x 777606 x 648008 x 486009 x 4320010 x 3888012 x 3240015 x 2592016 x 2430018 x 2160020 x 1944024 x 1620025 x 1555227 x 1440030 x 1296032 x 1215036 x 1080040 x 972045 x 864048 x 810050 x 777654 x 720060 x 648064 x 607572 x 540075 x 518480 x 486081 x 480090 x 432096 x 4050100 x 3888108 x 3600120 x 3240135 x 2880144 x 2700150 x 2592160 x 2430162 x 2400180 x 2160192 x 2025200 x 1944216 x 1800225 x 1728240 x 1620243 x 1600270 x 1440288 x 1350300 x 1296320 x 1215324 x 1200360 x 1080400 x 972405 x 960432 x 900450 x 864480 x 810486 x 800540 x 720576 x 675600 x 648
Negative: -1 x -388800-2 x -194400-3 x -129600-4 x -97200-5 x -77760-6 x -64800-8 x -48600-9 x -43200-10 x -38880-12 x -32400-15 x -25920-16 x -24300-18 x -21600-20 x -19440-24 x -16200-25 x -15552-27 x -14400-30 x -12960-32 x -12150-36 x -10800-40 x -9720-45 x -8640-48 x -8100-50 x -7776-54 x -7200-60 x -6480-64 x -6075-72 x -5400-75 x -5184-80 x -4860-81 x -4800-90 x -4320-96 x -4050-100 x -3888-108 x -3600-120 x -3240-135 x -2880-144 x -2700-150 x -2592-160 x -2430-162 x -2400-180 x -2160-192 x -2025-200 x -1944-216 x -1800-225 x -1728-240 x -1620-243 x -1600-270 x -1440-288 x -1350-300 x -1296-320 x -1215-324 x -1200-360 x -1080-400 x -972-405 x -960-432 x -900-450 x -864-480 x -810-486 x -800-540 x -720-576 x -675-600 x -648


How do I find the factor combinations of the number 388,800?

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 388,800, 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.

1 388,800
-1 -388,800

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 388,800.

Example:
1 x 388,800 = 388,800
and
-1 x -388,800 = 388,800
Notice both answers equal 388,800

With that explanation out of the way, let's continue. Next, we take the number 388,800 and divide it by 2:

388,800 ÷ 2 = 194,400

If the quotient is a whole number, then 2 and 194,400 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 2 194,400 388,800
-1 -2 -194,400 -388,800

Now, we try dividing 388,800 by 3:

388,800 ÷ 3 = 129,600

If the quotient is a whole number, then 3 and 129,600 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 3 129,600 194,400 388,800
-1 -2 -3 -129,600 -194,400 -388,800

Let's try dividing by 4:

388,800 ÷ 4 = 97,200

If the quotient is a whole number, then 4 and 97,200 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 97,200 129,600 194,400 388,800
-1 -2 -3 -4 -97,200 -129,600 -194,400 388,800
Keep dividing by the next highest number until you cannot divide anymore.

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

12345689101215161820242527303236404548505460647275808190961001081201351441501601621801922002162252402432702883003203243604004054324504804865405766006486757208008108649009609721,0801,2001,2151,2961,3501,4401,6001,6201,7281,8001,9442,0252,1602,4002,4302,5922,7002,8803,2403,6003,8884,0504,3204,8004,8605,1845,4006,0756,4807,2007,7768,1008,6409,72010,80012,15012,96014,40015,55216,20019,44021,60024,30025,92032,40038,88043,20048,60064,80077,76097,200129,600194,400388,800
-1-2-3-4-5-6-8-9-10-12-15-16-18-20-24-25-27-30-32-36-40-45-48-50-54-60-64-72-75-80-81-90-96-100-108-120-135-144-150-160-162-180-192-200-216-225-240-243-270-288-300-320-324-360-400-405-432-450-480-486-540-576-600-648-675-720-800-810-864-900-960-972-1,080-1,200-1,215-1,296-1,350-1,440-1,600-1,620-1,728-1,800-1,944-2,025-2,160-2,400-2,430-2,592-2,700-2,880-3,240-3,600-3,888-4,050-4,320-4,800-4,860-5,184-5,400-6,075-6,480-7,200-7,776-8,100-8,640-9,720-10,800-12,150-12,960-14,400-15,552-16,200-19,440-21,600-24,300-25,920-32,400-38,880-43,200-48,600-64,800-77,760-97,200-129,600-194,400-388,800

More Examples

Here are some more numbers to try:

388,798388,799388,801388,802
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