Q: What are the factor combinations of the number 23,688,360?

 A:
Positive:   1 x 236883602 x 118441803 x 78961204 x 59220905 x 47376726 x 39480608 x 29610459 x 263204010 x 236883612 x 197403015 x 157922418 x 131602020 x 118441824 x 98701529 x 81684030 x 78961236 x 65801040 x 59220945 x 52640858 x 40842060 x 39480672 x 32900587 x 27228090 x 263204116 x 204210120 x 197403145 x 163368174 x 136140180 x 131602232 x 102105261 x 90760290 x 81684348 x 68070360 x 65801435 x 54456522 x 45380580 x 40842696 x 34035870 x 272281044 x 226901160 x 204211305 x 181521740 x 136142088 x 113452269 x 104402610 x 90763480 x 68074538 x 5220
Negative: -1 x -23688360-2 x -11844180-3 x -7896120-4 x -5922090-5 x -4737672-6 x -3948060-8 x -2961045-9 x -2632040-10 x -2368836-12 x -1974030-15 x -1579224-18 x -1316020-20 x -1184418-24 x -987015-29 x -816840-30 x -789612-36 x -658010-40 x -592209-45 x -526408-58 x -408420-60 x -394806-72 x -329005-87 x -272280-90 x -263204-116 x -204210-120 x -197403-145 x -163368-174 x -136140-180 x -131602-232 x -102105-261 x -90760-290 x -81684-348 x -68070-360 x -65801-435 x -54456-522 x -45380-580 x -40842-696 x -34035-870 x -27228-1044 x -22690-1160 x -20421-1305 x -18152-1740 x -13614-2088 x -11345-2269 x -10440-2610 x -9076-3480 x -6807-4538 x -5220


How do I find the factor combinations of the number 23,688,360?

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 23,688,360, 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 23,688,360
-1 -23,688,360

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 23,688,360.

Example:
1 x 23,688,360 = 23,688,360
and
-1 x -23,688,360 = 23,688,360
Notice both answers equal 23,688,360

With that explanation out of the way, let's continue. Next, we take the number 23,688,360 and divide it by 2:

23,688,360 ÷ 2 = 11,844,180

If the quotient is a whole number, then 2 and 11,844,180 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 11,844,180 23,688,360
-1 -2 -11,844,180 -23,688,360

Now, we try dividing 23,688,360 by 3:

23,688,360 ÷ 3 = 7,896,120

If the quotient is a whole number, then 3 and 7,896,120 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 7,896,120 11,844,180 23,688,360
-1 -2 -3 -7,896,120 -11,844,180 -23,688,360

Let's try dividing by 4:

23,688,360 ÷ 4 = 5,922,090

If the quotient is a whole number, then 4 and 5,922,090 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 5,922,090 7,896,120 11,844,180 23,688,360
-1 -2 -3 -4 -5,922,090 -7,896,120 -11,844,180 23,688,360
Keep dividing by the next highest number until you cannot divide anymore.

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

12345689101215182024293036404558607287901161201451741802322612903483604355225806968701,0441,1601,3051,7402,0882,2692,6103,4804,5385,2206,8079,07610,44011,34513,61418,15220,42122,69027,22834,03540,84245,38054,45665,80168,07081,68490,760102,105131,602136,140163,368197,403204,210263,204272,280329,005394,806408,420526,408592,209658,010789,612816,840987,0151,184,4181,316,0201,579,2241,974,0302,368,8362,632,0402,961,0453,948,0604,737,6725,922,0907,896,12011,844,18023,688,360
-1-2-3-4-5-6-8-9-10-12-15-18-20-24-29-30-36-40-45-58-60-72-87-90-116-120-145-174-180-232-261-290-348-360-435-522-580-696-870-1,044-1,160-1,305-1,740-2,088-2,269-2,610-3,480-4,538-5,220-6,807-9,076-10,440-11,345-13,614-18,152-20,421-22,690-27,228-34,035-40,842-45,380-54,456-65,801-68,070-81,684-90,760-102,105-131,602-136,140-163,368-197,403-204,210-263,204-272,280-329,005-394,806-408,420-526,408-592,209-658,010-789,612-816,840-987,015-1,184,418-1,316,020-1,579,224-1,974,030-2,368,836-2,632,040-2,961,045-3,948,060-4,737,672-5,922,090-7,896,120-11,844,180-23,688,360

More Examples

Here are some more numbers to try:

23,688,35823,688,35923,688,36123,688,362
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