Q: What are the factor combinations of the number 42,103,523?

 A:
Positive:   1 x 421035237 x 601478911 x 382759377 x 546799121 x 347963847 x 497091331 x 316334519 x 9317
Negative: -1 x -42103523-7 x -6014789-11 x -3827593-77 x -546799-121 x -347963-847 x -49709-1331 x -31633-4519 x -9317


How do I find the factor combinations of the number 42,103,523?

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 42,103,523, 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 42,103,523
-1 -42,103,523

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 42,103,523.

Example:
1 x 42,103,523 = 42,103,523
and
-1 x -42,103,523 = 42,103,523
Notice both answers equal 42,103,523

With that explanation out of the way, let's continue. Next, we take the number 42,103,523 and divide it by 2:

42,103,523 ÷ 2 = 21,051,761.5

If the quotient is a whole number, then 2 and 21,051,761.5 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 42,103,523
-1 -42,103,523

Now, we try dividing 42,103,523 by 3:

42,103,523 ÷ 3 = 14,034,507.6667

If the quotient is a whole number, then 3 and 14,034,507.6667 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 42,103,523
-1 -42,103,523

Let's try dividing by 4:

42,103,523 ÷ 4 = 10,525,880.75

If the quotient is a whole number, then 4 and 10,525,880.75 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 42,103,523
-1 42,103,523
Keep dividing by the next highest number until you cannot divide anymore.

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

1711771218471,3314,5199,31731,63349,709347,963546,7993,827,5936,014,78942,103,523
-1-7-11-77-121-847-1,331-4,519-9,317-31,633-49,709-347,963-546,799-3,827,593-6,014,789-42,103,523

More Examples

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