Q: What are the factor combinations of the number 21,000,960?

 A:
Positive:   1 x 210009602 x 105004803 x 70003204 x 52502405 x 42001926 x 35001608 x 26251209 x 233344010 x 210009612 x 175008015 x 140006416 x 131256018 x 116672020 x 105004824 x 87504030 x 70003232 x 65628036 x 58336040 x 52502445 x 46668848 x 43752060 x 35001664 x 32814072 x 29168080 x 26251290 x 23334496 x 218760120 x 175008128 x 164070144 x 145840160 x 131256180 x 116672192 x 109380240 x 87504256 x 82035288 x 72920320 x 65628360 x 58336384 x 54690480 x 43752576 x 36460640 x 32814720 x 29168768 x 27345960 x 218761152 x 182301280 x 164071440 x 145841823 x 115201920 x 109382304 x 91152880 x 72923646 x 57603840 x 5469
Negative: -1 x -21000960-2 x -10500480-3 x -7000320-4 x -5250240-5 x -4200192-6 x -3500160-8 x -2625120-9 x -2333440-10 x -2100096-12 x -1750080-15 x -1400064-16 x -1312560-18 x -1166720-20 x -1050048-24 x -875040-30 x -700032-32 x -656280-36 x -583360-40 x -525024-45 x -466688-48 x -437520-60 x -350016-64 x -328140-72 x -291680-80 x -262512-90 x -233344-96 x -218760-120 x -175008-128 x -164070-144 x -145840-160 x -131256-180 x -116672-192 x -109380-240 x -87504-256 x -82035-288 x -72920-320 x -65628-360 x -58336-384 x -54690-480 x -43752-576 x -36460-640 x -32814-720 x -29168-768 x -27345-960 x -21876-1152 x -18230-1280 x -16407-1440 x -14584-1823 x -11520-1920 x -10938-2304 x -9115-2880 x -7292-3646 x -5760-3840 x -5469


How do I find the factor combinations of the number 21,000,960?

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 21,000,960, 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 21,000,960
-1 -21,000,960

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 21,000,960.

Example:
1 x 21,000,960 = 21,000,960
and
-1 x -21,000,960 = 21,000,960
Notice both answers equal 21,000,960

With that explanation out of the way, let's continue. Next, we take the number 21,000,960 and divide it by 2:

21,000,960 ÷ 2 = 10,500,480

If the quotient is a whole number, then 2 and 10,500,480 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 10,500,480 21,000,960
-1 -2 -10,500,480 -21,000,960

Now, we try dividing 21,000,960 by 3:

21,000,960 ÷ 3 = 7,000,320

If the quotient is a whole number, then 3 and 7,000,320 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 7,000,320 10,500,480 21,000,960
-1 -2 -3 -7,000,320 -10,500,480 -21,000,960

Let's try dividing by 4:

21,000,960 ÷ 4 = 5,250,240

If the quotient is a whole number, then 4 and 5,250,240 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 5,250,240 7,000,320 10,500,480 21,000,960
-1 -2 -3 -4 -5,250,240 -7,000,320 -10,500,480 21,000,960
Keep dividing by the next highest number until you cannot divide anymore.

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

12345689101215161820243032364045486064728090961201281441601801922402562883203603844805766407207689601,1521,2801,4401,8231,9202,3042,8803,6463,8405,4695,7607,2929,11510,93811,52014,58416,40718,23021,87627,34529,16832,81436,46043,75254,69058,33665,62872,92082,03587,504109,380116,672131,256145,840164,070175,008218,760233,344262,512291,680328,140350,016437,520466,688525,024583,360656,280700,032875,0401,050,0481,166,7201,312,5601,400,0641,750,0802,100,0962,333,4402,625,1203,500,1604,200,1925,250,2407,000,32010,500,48021,000,960
-1-2-3-4-5-6-8-9-10-12-15-16-18-20-24-30-32-36-40-45-48-60-64-72-80-90-96-120-128-144-160-180-192-240-256-288-320-360-384-480-576-640-720-768-960-1,152-1,280-1,440-1,823-1,920-2,304-2,880-3,646-3,840-5,469-5,760-7,292-9,115-10,938-11,520-14,584-16,407-18,230-21,876-27,345-29,168-32,814-36,460-43,752-54,690-58,336-65,628-72,920-82,035-87,504-109,380-116,672-131,256-145,840-164,070-175,008-218,760-233,344-262,512-291,680-328,140-350,016-437,520-466,688-525,024-583,360-656,280-700,032-875,040-1,050,048-1,166,720-1,312,560-1,400,064-1,750,080-2,100,096-2,333,440-2,625,120-3,500,160-4,200,192-5,250,240-7,000,320-10,500,480-21,000,960

More Examples

Here are some more numbers to try:

21,000,95821,000,95921,000,96121,000,962
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