Q: What are the factor combinations of the number 78,120?

 A:
Positive:   1 x 781202 x 390603 x 260404 x 195305 x 156246 x 130207 x 111608 x 97659 x 868010 x 781212 x 651014 x 558015 x 520818 x 434020 x 390621 x 372024 x 325528 x 279030 x 260431 x 252035 x 223236 x 217040 x 195342 x 186045 x 173656 x 139560 x 130262 x 126063 x 124070 x 111672 x 108584 x 93090 x 86893 x 840105 x 744120 x 651124 x 630126 x 620140 x 558155 x 504168 x 465180 x 434186 x 420210 x 372217 x 360248 x 315252 x 310279 x 280
Negative: -1 x -78120-2 x -39060-3 x -26040-4 x -19530-5 x -15624-6 x -13020-7 x -11160-8 x -9765-9 x -8680-10 x -7812-12 x -6510-14 x -5580-15 x -5208-18 x -4340-20 x -3906-21 x -3720-24 x -3255-28 x -2790-30 x -2604-31 x -2520-35 x -2232-36 x -2170-40 x -1953-42 x -1860-45 x -1736-56 x -1395-60 x -1302-62 x -1260-63 x -1240-70 x -1116-72 x -1085-84 x -930-90 x -868-93 x -840-105 x -744-120 x -651-124 x -630-126 x -620-140 x -558-155 x -504-168 x -465-180 x -434-186 x -420-210 x -372-217 x -360-248 x -315-252 x -310-279 x -280


How do I find the factor combinations of the number 78,120?

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 78,120, 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 78,120
-1 -78,120

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 78,120.

Example:
1 x 78,120 = 78,120
and
-1 x -78,120 = 78,120
Notice both answers equal 78,120

With that explanation out of the way, let's continue. Next, we take the number 78,120 and divide it by 2:

78,120 ÷ 2 = 39,060

If the quotient is a whole number, then 2 and 39,060 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 39,060 78,120
-1 -2 -39,060 -78,120

Now, we try dividing 78,120 by 3:

78,120 ÷ 3 = 26,040

If the quotient is a whole number, then 3 and 26,040 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 26,040 39,060 78,120
-1 -2 -3 -26,040 -39,060 -78,120

Let's try dividing by 4:

78,120 ÷ 4 = 19,530

If the quotient is a whole number, then 4 and 19,530 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 19,530 26,040 39,060 78,120
-1 -2 -3 -4 -19,530 -26,040 -39,060 78,120
Keep dividing by the next highest number until you cannot divide anymore.

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

123456789101214151820212428303135364042455660626370728490931051201241261401551681801862102172482522792803103153603724204344655045586206306517448408689301,0851,1161,2401,2601,3021,3951,7361,8601,9532,1702,2322,5202,6042,7903,2553,7203,9064,3405,2085,5806,5107,8128,6809,76511,16013,02015,62419,53026,04039,06078,120
-1-2-3-4-5-6-7-8-9-10-12-14-15-18-20-21-24-28-30-31-35-36-40-42-45-56-60-62-63-70-72-84-90-93-105-120-124-126-140-155-168-180-186-210-217-248-252-279-280-310-315-360-372-420-434-465-504-558-620-630-651-744-840-868-930-1,085-1,116-1,240-1,260-1,302-1,395-1,736-1,860-1,953-2,170-2,232-2,520-2,604-2,790-3,255-3,720-3,906-4,340-5,208-5,580-6,510-7,812-8,680-9,765-11,160-13,020-15,624-19,530-26,040-39,060-78,120

More Examples

Here are some more numbers to try:

78,11878,11978,12178,122
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