Q: What are the factor combinations of the number 42,317,405?

 A:
Positive:   1 x 423174055 x 846348113 x 325518565 x 651037439 x 963951483 x 285352195 x 192795707 x 7415
Negative: -1 x -42317405-5 x -8463481-13 x -3255185-65 x -651037-439 x -96395-1483 x -28535-2195 x -19279-5707 x -7415


How do I find the factor combinations of the number 42,317,405?

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 42,317,405, 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 42,317,405
-1 -42,317,405

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 42,317,405.

Example:
1 x 42,317,405 = 42,317,405
and
-1 x -42,317,405 = 42,317,405
Notice both answers equal 42,317,405

With that explanation out of the way, let's continue. Next, we take the number 42,317,405 and divide it by 2:

42,317,405 ÷ 2 = 21,158,702.5

If the quotient is a whole number, then 2 and 21,158,702.5 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 42,317,405
-1 -42,317,405

Now, we try dividing 42,317,405 by 3:

42,317,405 ÷ 3 = 14,105,801.6667

If the quotient is a whole number, then 3 and 14,105,801.6667 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 42,317,405
-1 -42,317,405

Let's try dividing by 4:

42,317,405 ÷ 4 = 10,579,351.25

If the quotient is a whole number, then 4 and 10,579,351.25 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 42,317,405
-1 42,317,405
Keep dividing by the next highest number until you cannot divide anymore.

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

1513654391,4832,1955,7077,41519,27928,53596,395651,0373,255,1858,463,48142,317,405
-1-5-13-65-439-1,483-2,195-5,707-7,415-19,279-28,535-96,395-651,037-3,255,185-8,463,481-42,317,405

More Examples

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