Q: What are the factor combinations of the number 175,525?

 A:
Positive:   1 x 1755255 x 351057 x 2507517 x 1032525 x 702135 x 501559 x 297585 x 2065119 x 1475175 x 1003295 x 595413 x 425
Negative: -1 x -175525-5 x -35105-7 x -25075-17 x -10325-25 x -7021-35 x -5015-59 x -2975-85 x -2065-119 x -1475-175 x -1003-295 x -595-413 x -425


How do I find the factor combinations of the number 175,525?

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 175,525, 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.

1 175,525
-1 -175,525

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 175,525.

Example:
1 x 175,525 = 175,525
and
-1 x -175,525 = 175,525
Notice both answers equal 175,525

With that explanation out of the way, let's continue. Next, we take the number 175,525 and divide it by 2:

175,525 ÷ 2 = 87,762.5

If the quotient is a whole number, then 2 and 87,762.5 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:

1 175,525
-1 -175,525

Now, we try dividing 175,525 by 3:

175,525 ÷ 3 = 58,508.3333

If the quotient is a whole number, then 3 and 58,508.3333 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:

1 175,525
-1 -175,525

Let's try dividing by 4:

175,525 ÷ 4 = 43,881.25

If the quotient is a whole number, then 4 and 43,881.25 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:

1 175,525
-1 175,525
Keep dividing by the next highest number until you cannot divide anymore.

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

15717253559851191752954134255951,0031,4752,0652,9755,0157,02110,32525,07535,105175,525
-1-5-7-17-25-35-59-85-119-175-295-413-425-595-1,003-1,475-2,065-2,975-5,015-7,021-10,325-25,075-35,105-175,525

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