Q: What are the factor combinations of the number 35,252,525?

 A:
Positive:   1 x 352525255 x 70505057 x 503607511 x 320477525 x 141010135 x 100721555 x 64095577 x 457825175 x 201443275 x 128191385 x 915651925 x 18313
Negative: -1 x -35252525-5 x -7050505-7 x -5036075-11 x -3204775-25 x -1410101-35 x -1007215-55 x -640955-77 x -457825-175 x -201443-275 x -128191-385 x -91565-1925 x -18313


How do I find the factor combinations of the number 35,252,525?

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 35,252,525, 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 35,252,525
-1 -35,252,525

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 35,252,525.

Example:
1 x 35,252,525 = 35,252,525
and
-1 x -35,252,525 = 35,252,525
Notice both answers equal 35,252,525

With that explanation out of the way, let's continue. Next, we take the number 35,252,525 and divide it by 2:

35,252,525 ÷ 2 = 17,626,262.5

If the quotient is a whole number, then 2 and 17,626,262.5 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 35,252,525
-1 -35,252,525

Now, we try dividing 35,252,525 by 3:

35,252,525 ÷ 3 = 11,750,841.6667

If the quotient is a whole number, then 3 and 11,750,841.6667 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 35,252,525
-1 -35,252,525

Let's try dividing by 4:

35,252,525 ÷ 4 = 8,813,131.25

If the quotient is a whole number, then 4 and 8,813,131.25 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 35,252,525
-1 35,252,525
Keep dividing by the next highest number until you cannot divide anymore.

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

15711253555771752753851,92518,31391,565128,191201,443457,825640,9551,007,2151,410,1013,204,7755,036,0757,050,50535,252,525
-1-5-7-11-25-35-55-77-175-275-385-1,925-18,313-91,565-128,191-201,443-457,825-640,955-1,007,215-1,410,101-3,204,775-5,036,075-7,050,505-35,252,525

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