Q: What are the factor combinations of the number 123,456,784?

 A:
Positive:   1 x 1234567842 x 617283924 x 308641968 x 1543209811 x 1122334416 x 771604922 x 561167243 x 287108844 x 280583686 x 143554488 x 1402918121 x 1020304172 x 717772176 x 701459242 x 510152344 x 358886473 x 261008484 x 255076688 x 179443946 x 130504968 x 1275381483 x 832481892 x 652521936 x 637692966 x 416243784 x 326265203 x 237285932 x 208127568 x 1631310406 x 11864
Negative: -1 x -123456784-2 x -61728392-4 x -30864196-8 x -15432098-11 x -11223344-16 x -7716049-22 x -5611672-43 x -2871088-44 x -2805836-86 x -1435544-88 x -1402918-121 x -1020304-172 x -717772-176 x -701459-242 x -510152-344 x -358886-473 x -261008-484 x -255076-688 x -179443-946 x -130504-968 x -127538-1483 x -83248-1892 x -65252-1936 x -63769-2966 x -41624-3784 x -32626-5203 x -23728-5932 x -20812-7568 x -16313-10406 x -11864


How do I find the factor combinations of the number 123,456,784?

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 123,456,784, 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.

1 123,456,784
-1 -123,456,784

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 123,456,784.

Example:
1 x 123,456,784 = 123,456,784
and
-1 x -123,456,784 = 123,456,784
Notice both answers equal 123,456,784

With that explanation out of the way, let's continue. Next, we take the number 123,456,784 and divide it by 2:

123,456,784 ÷ 2 = 61,728,392

If the quotient is a whole number, then 2 and 61,728,392 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 61,728,392 123,456,784
-1 -2 -61,728,392 -123,456,784

Now, we try dividing 123,456,784 by 3:

123,456,784 ÷ 3 = 41,152,261.3333

If the quotient is a whole number, then 3 and 41,152,261.3333 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 61,728,392 123,456,784
-1 -2 -61,728,392 -123,456,784

Let's try dividing by 4:

123,456,784 ÷ 4 = 30,864,196

If the quotient is a whole number, then 4 and 30,864,196 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 30,864,196 61,728,392 123,456,784
-1 -2 -4 -30,864,196 -61,728,392 123,456,784
Keep dividing by the next highest number until you cannot divide anymore.

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

1248111622434486881211721762423444734846889469681,4831,8921,9362,9663,7845,2035,9327,56810,40611,86416,31320,81223,72832,62641,62463,76965,25283,248127,538130,504179,443255,076261,008358,886510,152701,459717,7721,020,3041,402,9181,435,5442,805,8362,871,0885,611,6727,716,04911,223,34415,432,09830,864,19661,728,392123,456,784
-1-2-4-8-11-16-22-43-44-86-88-121-172-176-242-344-473-484-688-946-968-1,483-1,892-1,936-2,966-3,784-5,203-5,932-7,568-10,406-11,864-16,313-20,812-23,728-32,626-41,624-63,769-65,252-83,248-127,538-130,504-179,443-255,076-261,008-358,886-510,152-701,459-717,772-1,020,304-1,402,918-1,435,544-2,805,836-2,871,088-5,611,672-7,716,049-11,223,344-15,432,098-30,864,196-61,728,392-123,456,784

More Examples

Here are some more numbers to try:

123,456,782123,456,783123,456,785123,456,786
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