Q: What are the factor combinations of the number 735,120?

 A:
Positive:   1 x 7351202 x 3675603 x 2450404 x 1837805 x 1470246 x 1225208 x 918909 x 8168010 x 7351212 x 6126015 x 4900816 x 4594518 x 4084020 x 3675624 x 3063030 x 2450436 x 2042040 x 1837845 x 1633648 x 1531560 x 1225272 x 1021080 x 918990 x 8168120 x 6126144 x 5105180 x 4084240 x 3063360 x 2042720 x 1021
Negative: -1 x -735120-2 x -367560-3 x -245040-4 x -183780-5 x -147024-6 x -122520-8 x -91890-9 x -81680-10 x -73512-12 x -61260-15 x -49008-16 x -45945-18 x -40840-20 x -36756-24 x -30630-30 x -24504-36 x -20420-40 x -18378-45 x -16336-48 x -15315-60 x -12252-72 x -10210-80 x -9189-90 x -8168-120 x -6126-144 x -5105-180 x -4084-240 x -3063-360 x -2042-720 x -1021


How do I find the factor combinations of the number 735,120?

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 735,120, 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.

1 735,120
-1 -735,120

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 735,120.

Example:
1 x 735,120 = 735,120
and
-1 x -735,120 = 735,120
Notice both answers equal 735,120

With that explanation out of the way, let's continue. Next, we take the number 735,120 and divide it by 2:

735,120 ÷ 2 = 367,560

If the quotient is a whole number, then 2 and 367,560 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 2 367,560 735,120
-1 -2 -367,560 -735,120

Now, we try dividing 735,120 by 3:

735,120 ÷ 3 = 245,040

If the quotient is a whole number, then 3 and 245,040 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 3 245,040 367,560 735,120
-1 -2 -3 -245,040 -367,560 -735,120

Let's try dividing by 4:

735,120 ÷ 4 = 183,780

If the quotient is a whole number, then 4 and 183,780 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 4 183,780 245,040 367,560 735,120
-1 -2 -3 -4 -183,780 -245,040 -367,560 735,120
Keep dividing by the next highest number until you cannot divide anymore.

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

12345689101215161820243036404548607280901201441802403607201,0212,0423,0634,0845,1056,1268,1689,18910,21012,25215,31516,33618,37820,42024,50430,63036,75640,84045,94549,00861,26073,51281,68091,890122,520147,024183,780245,040367,560735,120
-1-2-3-4-5-6-8-9-10-12-15-16-18-20-24-30-36-40-45-48-60-72-80-90-120-144-180-240-360-720-1,021-2,042-3,063-4,084-5,105-6,126-8,168-9,189-10,210-12,252-15,315-16,336-18,378-20,420-24,504-30,630-36,756-40,840-45,945-49,008-61,260-73,512-81,680-91,890-122,520-147,024-183,780-245,040-367,560-735,120

More Examples

Here are some more numbers to try:

735,118735,119735,121735,122
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