Q: What are the factor combinations of the number 3,698,640?

 A:
Positive:   1 x 36986402 x 18493203 x 12328804 x 9246605 x 7397286 x 6164408 x 4623309 x 41096010 x 36986411 x 33624012 x 30822015 x 24657616 x 23116518 x 20548020 x 18493222 x 16812024 x 15411030 x 12328833 x 11208036 x 10274040 x 9246644 x 8406045 x 8219248 x 7705555 x 6724860 x 6164466 x 5604072 x 5137080 x 4623388 x 4203090 x 4109699 x 37360110 x 33624120 x 30822132 x 28020144 x 25685165 x 22416176 x 21015180 x 20548198 x 18680220 x 16812240 x 15411264 x 14010330 x 11208360 x 10274396 x 9340440 x 8406467 x 7920495 x 7472528 x 7005660 x 5604720 x 5137792 x 4670880 x 4203934 x 3960990 x 37361320 x 28021401 x 26401584 x 23351868 x 1980
Negative: -1 x -3698640-2 x -1849320-3 x -1232880-4 x -924660-5 x -739728-6 x -616440-8 x -462330-9 x -410960-10 x -369864-11 x -336240-12 x -308220-15 x -246576-16 x -231165-18 x -205480-20 x -184932-22 x -168120-24 x -154110-30 x -123288-33 x -112080-36 x -102740-40 x -92466-44 x -84060-45 x -82192-48 x -77055-55 x -67248-60 x -61644-66 x -56040-72 x -51370-80 x -46233-88 x -42030-90 x -41096-99 x -37360-110 x -33624-120 x -30822-132 x -28020-144 x -25685-165 x -22416-176 x -21015-180 x -20548-198 x -18680-220 x -16812-240 x -15411-264 x -14010-330 x -11208-360 x -10274-396 x -9340-440 x -8406-467 x -7920-495 x -7472-528 x -7005-660 x -5604-720 x -5137-792 x -4670-880 x -4203-934 x -3960-990 x -3736-1320 x -2802-1401 x -2640-1584 x -2335-1868 x -1980


How do I find the factor combinations of the number 3,698,640?

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 3,698,640, 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 3,698,640
-1 -3,698,640

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 3,698,640.

Example:
1 x 3,698,640 = 3,698,640
and
-1 x -3,698,640 = 3,698,640
Notice both answers equal 3,698,640

With that explanation out of the way, let's continue. Next, we take the number 3,698,640 and divide it by 2:

3,698,640 ÷ 2 = 1,849,320

If the quotient is a whole number, then 2 and 1,849,320 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 1,849,320 3,698,640
-1 -2 -1,849,320 -3,698,640

Now, we try dividing 3,698,640 by 3:

3,698,640 ÷ 3 = 1,232,880

If the quotient is a whole number, then 3 and 1,232,880 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 1,232,880 1,849,320 3,698,640
-1 -2 -3 -1,232,880 -1,849,320 -3,698,640

Let's try dividing by 4:

3,698,640 ÷ 4 = 924,660

If the quotient is a whole number, then 4 and 924,660 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 4 924,660 1,232,880 1,849,320 3,698,640
-1 -2 -3 -4 -924,660 -1,232,880 -1,849,320 3,698,640
Keep dividing by the next highest number until you cannot divide anymore.

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

123456891011121516182022243033364044454855606672808890991101201321441651761801982202402643303603964404674955286607207928809349901,3201,4011,5841,8681,9802,3352,6402,8023,7363,9604,2034,6705,1375,6047,0057,4727,9208,4069,34010,27411,20814,01015,41116,81218,68020,54821,01522,41625,68528,02030,82233,62437,36041,09642,03046,23351,37056,04061,64467,24877,05582,19284,06092,466102,740112,080123,288154,110168,120184,932205,480231,165246,576308,220336,240369,864410,960462,330616,440739,728924,6601,232,8801,849,3203,698,640
-1-2-3-4-5-6-8-9-10-11-12-15-16-18-20-22-24-30-33-36-40-44-45-48-55-60-66-72-80-88-90-99-110-120-132-144-165-176-180-198-220-240-264-330-360-396-440-467-495-528-660-720-792-880-934-990-1,320-1,401-1,584-1,868-1,980-2,335-2,640-2,802-3,736-3,960-4,203-4,670-5,137-5,604-7,005-7,472-7,920-8,406-9,340-10,274-11,208-14,010-15,411-16,812-18,680-20,548-21,015-22,416-25,685-28,020-30,822-33,624-37,360-41,096-42,030-46,233-51,370-56,040-61,644-67,248-77,055-82,192-84,060-92,466-102,740-112,080-123,288-154,110-168,120-184,932-205,480-231,165-246,576-308,220-336,240-369,864-410,960-462,330-616,440-739,728-924,660-1,232,880-1,849,320-3,698,640

More Examples

Here are some more numbers to try:

3,698,6383,698,6393,698,6413,698,642
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