Q: What are the factor combinations of the number 1,524,120?

 A:
Positive:   1 x 15241202 x 7620603 x 5080404 x 3810305 x 3048246 x 2540208 x 19051510 x 15241212 x 12701013 x 11724015 x 10160820 x 7620624 x 6350526 x 5862030 x 5080439 x 3908040 x 3810352 x 2931060 x 2540265 x 2344878 x 19540104 x 14655120 x 12701130 x 11724156 x 9770195 x 7816260 x 5862312 x 4885390 x 3908520 x 2931780 x 1954977 x 1560
Negative: -1 x -1524120-2 x -762060-3 x -508040-4 x -381030-5 x -304824-6 x -254020-8 x -190515-10 x -152412-12 x -127010-13 x -117240-15 x -101608-20 x -76206-24 x -63505-26 x -58620-30 x -50804-39 x -39080-40 x -38103-52 x -29310-60 x -25402-65 x -23448-78 x -19540-104 x -14655-120 x -12701-130 x -11724-156 x -9770-195 x -7816-260 x -5862-312 x -4885-390 x -3908-520 x -2931-780 x -1954-977 x -1560


How do I find the factor combinations of the number 1,524,120?

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 1,524,120, 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 1,524,120
-1 -1,524,120

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 1,524,120.

Example:
1 x 1,524,120 = 1,524,120
and
-1 x -1,524,120 = 1,524,120
Notice both answers equal 1,524,120

With that explanation out of the way, let's continue. Next, we take the number 1,524,120 and divide it by 2:

1,524,120 ÷ 2 = 762,060

If the quotient is a whole number, then 2 and 762,060 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 2 762,060 1,524,120
-1 -2 -762,060 -1,524,120

Now, we try dividing 1,524,120 by 3:

1,524,120 ÷ 3 = 508,040

If the quotient is a whole number, then 3 and 508,040 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 3 508,040 762,060 1,524,120
-1 -2 -3 -508,040 -762,060 -1,524,120

Let's try dividing by 4:

1,524,120 ÷ 4 = 381,030

If the quotient is a whole number, then 4 and 381,030 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 4 381,030 508,040 762,060 1,524,120
-1 -2 -3 -4 -381,030 -508,040 -762,060 1,524,120
Keep dividing by the next highest number until you cannot divide anymore.

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

123456810121315202426303940526065781041201301561952603123905207809771,5601,9542,9313,9084,8855,8627,8169,77011,72412,70114,65519,54023,44825,40229,31038,10339,08050,80458,62063,50576,206101,608117,240127,010152,412190,515254,020304,824381,030508,040762,0601,524,120
-1-2-3-4-5-6-8-10-12-13-15-20-24-26-30-39-40-52-60-65-78-104-120-130-156-195-260-312-390-520-780-977-1,560-1,954-2,931-3,908-4,885-5,862-7,816-9,770-11,724-12,701-14,655-19,540-23,448-25,402-29,310-38,103-39,080-50,804-58,620-63,505-76,206-101,608-117,240-127,010-152,412-190,515-254,020-304,824-381,030-508,040-762,060-1,524,120

More Examples

Here are some more numbers to try:

1,524,1181,524,1191,524,1211,524,122
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