Q: What are the factor combinations of the number 274,872,320?

 A:
Positive:   1 x 2748723202 x 1374361604 x 687180805 x 549744648 x 3435904010 x 2748723216 x 1717952017 x 1616896020 x 1374361632 x 858976034 x 808448040 x 687180864 x 429488068 x 404224080 x 343590485 x 3233792128 x 2147440136 x 2021120160 x 1717952170 x 1616896256 x 1073720272 x 1010560320 x 858976340 x 808448512 x 536860544 x 505280640 x 429488680 x 4042241024 x 2684301088 x 2526401280 x 2147441360 x 2021121579 x 1740802048 x 1342152176 x 1263202560 x 1073722720 x 1010563158 x 870404352 x 631605120 x 536865440 x 505286316 x 435207895 x 348168704 x 3158010240 x 2684310880 x 2526412632 x 2176015790 x 17408
Negative: -1 x -274872320-2 x -137436160-4 x -68718080-5 x -54974464-8 x -34359040-10 x -27487232-16 x -17179520-17 x -16168960-20 x -13743616-32 x -8589760-34 x -8084480-40 x -6871808-64 x -4294880-68 x -4042240-80 x -3435904-85 x -3233792-128 x -2147440-136 x -2021120-160 x -1717952-170 x -1616896-256 x -1073720-272 x -1010560-320 x -858976-340 x -808448-512 x -536860-544 x -505280-640 x -429488-680 x -404224-1024 x -268430-1088 x -252640-1280 x -214744-1360 x -202112-1579 x -174080-2048 x -134215-2176 x -126320-2560 x -107372-2720 x -101056-3158 x -87040-4352 x -63160-5120 x -53686-5440 x -50528-6316 x -43520-7895 x -34816-8704 x -31580-10240 x -26843-10880 x -25264-12632 x -21760-15790 x -17408


How do I find the factor combinations of the number 274,872,320?

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 274,872,320, 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.

1 274,872,320
-1 -274,872,320

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 274,872,320.

Example:
1 x 274,872,320 = 274,872,320
and
-1 x -274,872,320 = 274,872,320
Notice both answers equal 274,872,320

With that explanation out of the way, let's continue. Next, we take the number 274,872,320 and divide it by 2:

274,872,320 ÷ 2 = 137,436,160

If the quotient is a whole number, then 2 and 137,436,160 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 2 137,436,160 274,872,320
-1 -2 -137,436,160 -274,872,320

Now, we try dividing 274,872,320 by 3:

274,872,320 ÷ 3 = 91,624,106.6667

If the quotient is a whole number, then 3 and 91,624,106.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

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

1 2 137,436,160 274,872,320
-1 -2 -137,436,160 -274,872,320

Let's try dividing by 4:

274,872,320 ÷ 4 = 68,718,080

If the quotient is a whole number, then 4 and 68,718,080 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 4 68,718,080 137,436,160 274,872,320
-1 -2 -4 -68,718,080 -137,436,160 274,872,320
Keep dividing by the next highest number until you cannot divide anymore.

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

1245810161720323440646880851281361601702562723203405125446406801,0241,0881,2801,3601,5792,0482,1762,5602,7203,1584,3525,1205,4406,3167,8958,70410,24010,88012,63215,79017,40821,76025,26426,84331,58034,81643,52050,52853,68663,16087,040101,056107,372126,320134,215174,080202,112214,744252,640268,430404,224429,488505,280536,860808,448858,9761,010,5601,073,7201,616,8961,717,9522,021,1202,147,4403,233,7923,435,9044,042,2404,294,8806,871,8088,084,4808,589,76013,743,61616,168,96017,179,52027,487,23234,359,04054,974,46468,718,080137,436,160274,872,320
-1-2-4-5-8-10-16-17-20-32-34-40-64-68-80-85-128-136-160-170-256-272-320-340-512-544-640-680-1,024-1,088-1,280-1,360-1,579-2,048-2,176-2,560-2,720-3,158-4,352-5,120-5,440-6,316-7,895-8,704-10,240-10,880-12,632-15,790-17,408-21,760-25,264-26,843-31,580-34,816-43,520-50,528-53,686-63,160-87,040-101,056-107,372-126,320-134,215-174,080-202,112-214,744-252,640-268,430-404,224-429,488-505,280-536,860-808,448-858,976-1,010,560-1,073,720-1,616,896-1,717,952-2,021,120-2,147,440-3,233,792-3,435,904-4,042,240-4,294,880-6,871,808-8,084,480-8,589,760-13,743,616-16,168,960-17,179,520-27,487,232-34,359,040-54,974,464-68,718,080-137,436,160-274,872,320

More Examples

Here are some more numbers to try:

274,872,318274,872,319274,872,321274,872,322
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