Q: What are the factor combinations of the number 42,103,135?

 A:
Positive:   1 x 421031355 x 842062717 x 247665567 x 62840585 x 495331335 x 1256811139 x 369655695 x 7393
Negative: -1 x -42103135-5 x -8420627-17 x -2476655-67 x -628405-85 x -495331-335 x -125681-1139 x -36965-5695 x -7393


How do I find the factor combinations of the number 42,103,135?

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 42,103,135, 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 42,103,135
-1 -42,103,135

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 42,103,135.

Example:
1 x 42,103,135 = 42,103,135
and
-1 x -42,103,135 = 42,103,135
Notice both answers equal 42,103,135

With that explanation out of the way, let's continue. Next, we take the number 42,103,135 and divide it by 2:

42,103,135 ÷ 2 = 21,051,567.5

If the quotient is a whole number, then 2 and 21,051,567.5 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 42,103,135
-1 -42,103,135

Now, we try dividing 42,103,135 by 3:

42,103,135 ÷ 3 = 14,034,378.3333

If the quotient is a whole number, then 3 and 14,034,378.3333 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 42,103,135
-1 -42,103,135

Let's try dividing by 4:

42,103,135 ÷ 4 = 10,525,783.75

If the quotient is a whole number, then 4 and 10,525,783.75 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 42,103,135
-1 42,103,135
Keep dividing by the next highest number until you cannot divide anymore.

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

151767853351,1395,6957,39336,965125,681495,331628,4052,476,6558,420,62742,103,135
-1-5-17-67-85-335-1,139-5,695-7,393-36,965-125,681-495,331-628,405-2,476,655-8,420,627-42,103,135

More Examples

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