Q: What are the factor combinations of the number 647,525?

 A:
Positive:   1 x 6475255 x 12950525 x 2590159 x 10975295 x 2195439 x 1475
Negative: -1 x -647525-5 x -129505-25 x -25901-59 x -10975-295 x -2195-439 x -1475


How do I find the factor combinations of the number 647,525?

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 647,525, 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.

1 647,525
-1 -647,525

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 647,525.

Example:
1 x 647,525 = 647,525
and
-1 x -647,525 = 647,525
Notice both answers equal 647,525

With that explanation out of the way, let's continue. Next, we take the number 647,525 and divide it by 2:

647,525 ÷ 2 = 323,762.5

If the quotient is a whole number, then 2 and 323,762.5 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:

1 647,525
-1 -647,525

Now, we try dividing 647,525 by 3:

647,525 ÷ 3 = 215,841.6667

If the quotient is a whole number, then 3 and 215,841.6667 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:

1 647,525
-1 -647,525

Let's try dividing by 4:

647,525 ÷ 4 = 161,881.25

If the quotient is a whole number, then 4 and 161,881.25 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:

1 647,525
-1 647,525
Keep dividing by the next highest number until you cannot divide anymore.

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

1525592954391,4752,19510,97525,901129,505647,525
-1-5-25-59-295-439-1,475-2,195-10,975-25,901-129,505-647,525

More Examples

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