Q: What are the factor combinations of the number 360,365,252?

 A:
Positive:   1 x 3603652522 x 1801826264 x 9009131313 x 2772040417 x 2119795626 x 1386020229 x 1242638834 x 1059897852 x 693010158 x 621319468 x 5299489116 x 3106597221 x 1630612377 x 955876442 x 815306493 x 730964754 x 477938884 x 407653986 x 3654821508 x 2389691972 x 1827416409 x 5622812818 x 2811414057 x 25636
Negative: -1 x -360365252-2 x -180182626-4 x -90091313-13 x -27720404-17 x -21197956-26 x -13860202-29 x -12426388-34 x -10598978-52 x -6930101-58 x -6213194-68 x -5299489-116 x -3106597-221 x -1630612-377 x -955876-442 x -815306-493 x -730964-754 x -477938-884 x -407653-986 x -365482-1508 x -238969-1972 x -182741-6409 x -56228-12818 x -28114-14057 x -25636


How do I find the factor combinations of the number 360,365,252?

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 360,365,252, 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.

1 360,365,252
-1 -360,365,252

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 360,365,252.

Example:
1 x 360,365,252 = 360,365,252
and
-1 x -360,365,252 = 360,365,252
Notice both answers equal 360,365,252

With that explanation out of the way, let's continue. Next, we take the number 360,365,252 and divide it by 2:

360,365,252 ÷ 2 = 180,182,626

If the quotient is a whole number, then 2 and 180,182,626 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 2 180,182,626 360,365,252
-1 -2 -180,182,626 -360,365,252

Now, we try dividing 360,365,252 by 3:

360,365,252 ÷ 3 = 120,121,750.6667

If the quotient is a whole number, then 3 and 120,121,750.6667 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 2 180,182,626 360,365,252
-1 -2 -180,182,626 -360,365,252

Let's try dividing by 4:

360,365,252 ÷ 4 = 90,091,313

If the quotient is a whole number, then 4 and 90,091,313 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 90,091,313 180,182,626 360,365,252
-1 -2 -4 -90,091,313 -180,182,626 360,365,252
Keep dividing by the next highest number until you cannot divide anymore.

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

12413172629345258681162213774424937548849861,5081,9726,40912,81814,05725,63628,11456,228182,741238,969365,482407,653477,938730,964815,306955,8761,630,6123,106,5975,299,4896,213,1946,930,10110,598,97812,426,38813,860,20221,197,95627,720,40490,091,313180,182,626360,365,252
-1-2-4-13-17-26-29-34-52-58-68-116-221-377-442-493-754-884-986-1,508-1,972-6,409-12,818-14,057-25,636-28,114-56,228-182,741-238,969-365,482-407,653-477,938-730,964-815,306-955,876-1,630,612-3,106,597-5,299,489-6,213,194-6,930,101-10,598,978-12,426,388-13,860,202-21,197,956-27,720,404-90,091,313-180,182,626-360,365,252

More Examples

Here are some more numbers to try:

360,365,250360,365,251360,365,253360,365,254
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