Q: What are the factor combinations of the number 649,475?

 A:
Positive:   1 x 6494755 x 12989525 x 2597983 x 7825313 x 2075415 x 1565
Negative: -1 x -649475-5 x -129895-25 x -25979-83 x -7825-313 x -2075-415 x -1565


How do I find the factor combinations of the number 649,475?

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 649,475, 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.

1 649,475
-1 -649,475

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 649,475.

Example:
1 x 649,475 = 649,475
and
-1 x -649,475 = 649,475
Notice both answers equal 649,475

With that explanation out of the way, let's continue. Next, we take the number 649,475 and divide it by 2:

649,475 ÷ 2 = 324,737.5

If the quotient is a whole number, then 2 and 324,737.5 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:

1 649,475
-1 -649,475

Now, we try dividing 649,475 by 3:

649,475 ÷ 3 = 216,491.6667

If the quotient is a whole number, then 3 and 216,491.6667 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:

1 649,475
-1 -649,475

Let's try dividing by 4:

649,475 ÷ 4 = 162,368.75

If the quotient is a whole number, then 4 and 162,368.75 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:

1 649,475
-1 649,475
Keep dividing by the next highest number until you cannot divide anymore.

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

1525833134151,5652,0757,82525,979129,895649,475
-1-5-25-83-313-415-1,565-2,075-7,825-25,979-129,895-649,475

More Examples

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