Q: What are the factor combinations of the number 34,807,680?

 A:
Positive:   1 x 348076802 x 174038403 x 116025604 x 87019205 x 69615366 x 58012808 x 43509609 x 386752010 x 348076812 x 290064015 x 232051216 x 217548018 x 193376020 x 174038424 x 145032030 x 116025632 x 108774036 x 96688040 x 87019245 x 77350448 x 72516060 x 58012864 x 54387072 x 48344080 x 43509690 x 38675296 x 362580120 x 290064128 x 271935144 x 241720160 x 217548180 x 193376192 x 181290240 x 145032288 x 120860320 x 108774360 x 96688384 x 90645480 x 72516576 x 60430640 x 54387720 x 48344960 x 362581152 x 302151440 x 241721920 x 181292880 x 120865760 x 6043
Negative: -1 x -34807680-2 x -17403840-3 x -11602560-4 x -8701920-5 x -6961536-6 x -5801280-8 x -4350960-9 x -3867520-10 x -3480768-12 x -2900640-15 x -2320512-16 x -2175480-18 x -1933760-20 x -1740384-24 x -1450320-30 x -1160256-32 x -1087740-36 x -966880-40 x -870192-45 x -773504-48 x -725160-60 x -580128-64 x -543870-72 x -483440-80 x -435096-90 x -386752-96 x -362580-120 x -290064-128 x -271935-144 x -241720-160 x -217548-180 x -193376-192 x -181290-240 x -145032-288 x -120860-320 x -108774-360 x -96688-384 x -90645-480 x -72516-576 x -60430-640 x -54387-720 x -48344-960 x -36258-1152 x -30215-1440 x -24172-1920 x -18129-2880 x -12086-5760 x -6043


How do I find the factor combinations of the number 34,807,680?

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 34,807,680, 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 34,807,680
-1 -34,807,680

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 34,807,680.

Example:
1 x 34,807,680 = 34,807,680
and
-1 x -34,807,680 = 34,807,680
Notice both answers equal 34,807,680

With that explanation out of the way, let's continue. Next, we take the number 34,807,680 and divide it by 2:

34,807,680 ÷ 2 = 17,403,840

If the quotient is a whole number, then 2 and 17,403,840 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 17,403,840 34,807,680
-1 -2 -17,403,840 -34,807,680

Now, we try dividing 34,807,680 by 3:

34,807,680 ÷ 3 = 11,602,560

If the quotient is a whole number, then 3 and 11,602,560 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 11,602,560 17,403,840 34,807,680
-1 -2 -3 -11,602,560 -17,403,840 -34,807,680

Let's try dividing by 4:

34,807,680 ÷ 4 = 8,701,920

If the quotient is a whole number, then 4 and 8,701,920 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 8,701,920 11,602,560 17,403,840 34,807,680
-1 -2 -3 -4 -8,701,920 -11,602,560 -17,403,840 34,807,680
Keep dividing by the next highest number until you cannot divide anymore.

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

12345689101215161820243032364045486064728090961201281441601801922402883203603844805766407209601,1521,4401,9202,8805,7606,04312,08618,12924,17230,21536,25848,34454,38760,43072,51690,64596,688108,774120,860145,032181,290193,376217,548241,720271,935290,064362,580386,752435,096483,440543,870580,128725,160773,504870,192966,8801,087,7401,160,2561,450,3201,740,3841,933,7602,175,4802,320,5122,900,6403,480,7683,867,5204,350,9605,801,2806,961,5368,701,92011,602,56017,403,84034,807,680
-1-2-3-4-5-6-8-9-10-12-15-16-18-20-24-30-32-36-40-45-48-60-64-72-80-90-96-120-128-144-160-180-192-240-288-320-360-384-480-576-640-720-960-1,152-1,440-1,920-2,880-5,760-6,043-12,086-18,129-24,172-30,215-36,258-48,344-54,387-60,430-72,516-90,645-96,688-108,774-120,860-145,032-181,290-193,376-217,548-241,720-271,935-290,064-362,580-386,752-435,096-483,440-543,870-580,128-725,160-773,504-870,192-966,880-1,087,740-1,160,256-1,450,320-1,740,384-1,933,760-2,175,480-2,320,512-2,900,640-3,480,768-3,867,520-4,350,960-5,801,280-6,961,536-8,701,920-11,602,560-17,403,840-34,807,680

More Examples

Here are some more numbers to try:

34,807,67834,807,67934,807,68134,807,682
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