Q: What are the factor combinations of the number 7,575,000?

 A:
Positive:   1 x 75750002 x 37875003 x 25250004 x 18937505 x 15150006 x 12625008 x 94687510 x 75750012 x 63125015 x 50500020 x 37875024 x 31562525 x 30300030 x 25250040 x 18937550 x 15150060 x 12625075 x 101000100 x 75750101 x 75000120 x 63125125 x 60600150 x 50500200 x 37875202 x 37500250 x 30300300 x 25250303 x 25000375 x 20200404 x 18750500 x 15150505 x 15000600 x 12625606 x 12500625 x 12120750 x 10100808 x 93751000 x 75751010 x 75001212 x 62501250 x 60601500 x 50501515 x 50001875 x 40402020 x 37502424 x 31252500 x 30302525 x 3000
Negative: -1 x -7575000-2 x -3787500-3 x -2525000-4 x -1893750-5 x -1515000-6 x -1262500-8 x -946875-10 x -757500-12 x -631250-15 x -505000-20 x -378750-24 x -315625-25 x -303000-30 x -252500-40 x -189375-50 x -151500-60 x -126250-75 x -101000-100 x -75750-101 x -75000-120 x -63125-125 x -60600-150 x -50500-200 x -37875-202 x -37500-250 x -30300-300 x -25250-303 x -25000-375 x -20200-404 x -18750-500 x -15150-505 x -15000-600 x -12625-606 x -12500-625 x -12120-750 x -10100-808 x -9375-1000 x -7575-1010 x -7500-1212 x -6250-1250 x -6060-1500 x -5050-1515 x -5000-1875 x -4040-2020 x -3750-2424 x -3125-2500 x -3030-2525 x -3000


How do I find the factor combinations of the number 7,575,000?

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 7,575,000, 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 7,575,000
-1 -7,575,000

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 7,575,000.

Example:
1 x 7,575,000 = 7,575,000
and
-1 x -7,575,000 = 7,575,000
Notice both answers equal 7,575,000

With that explanation out of the way, let's continue. Next, we take the number 7,575,000 and divide it by 2:

7,575,000 ÷ 2 = 3,787,500

If the quotient is a whole number, then 2 and 3,787,500 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 3,787,500 7,575,000
-1 -2 -3,787,500 -7,575,000

Now, we try dividing 7,575,000 by 3:

7,575,000 ÷ 3 = 2,525,000

If the quotient is a whole number, then 3 and 2,525,000 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 2,525,000 3,787,500 7,575,000
-1 -2 -3 -2,525,000 -3,787,500 -7,575,000

Let's try dividing by 4:

7,575,000 ÷ 4 = 1,893,750

If the quotient is a whole number, then 4 and 1,893,750 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 1,893,750 2,525,000 3,787,500 7,575,000
-1 -2 -3 -4 -1,893,750 -2,525,000 -3,787,500 7,575,000
Keep dividing by the next highest number until you cannot divide anymore.

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

123456810121520242530405060751001011201251502002022503003033754045005056006066257508081,0001,0101,2121,2501,5001,5151,8752,0202,4242,5002,5253,0003,0303,1253,7504,0405,0005,0506,0606,2507,5007,5759,37510,10012,12012,50012,62515,00015,15018,75020,20025,00025,25030,30037,50037,87550,50060,60063,12575,00075,750101,000126,250151,500189,375252,500303,000315,625378,750505,000631,250757,500946,8751,262,5001,515,0001,893,7502,525,0003,787,5007,575,000
-1-2-3-4-5-6-8-10-12-15-20-24-25-30-40-50-60-75-100-101-120-125-150-200-202-250-300-303-375-404-500-505-600-606-625-750-808-1,000-1,010-1,212-1,250-1,500-1,515-1,875-2,020-2,424-2,500-2,525-3,000-3,030-3,125-3,750-4,040-5,000-5,050-6,060-6,250-7,500-7,575-9,375-10,100-12,120-12,500-12,625-15,000-15,150-18,750-20,200-25,000-25,250-30,300-37,500-37,875-50,500-60,600-63,125-75,000-75,750-101,000-126,250-151,500-189,375-252,500-303,000-315,625-378,750-505,000-631,250-757,500-946,875-1,262,500-1,515,000-1,893,750-2,525,000-3,787,500-7,575,000

More Examples

Here are some more numbers to try:

7,574,9987,574,9997,575,0017,575,002
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