Q: What are the factor combinations of the number 42,103,435?

 A:
Positive:   1 x 421034355 x 842068711 x 382758555 x 765517239 x 1761651195 x 352332629 x 160153203 x 13145
Negative: -1 x -42103435-5 x -8420687-11 x -3827585-55 x -765517-239 x -176165-1195 x -35233-2629 x -16015-3203 x -13145


How do I find the factor combinations of the number 42,103,435?

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 42,103,435, 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 42,103,435
-1 -42,103,435

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 42,103,435.

Example:
1 x 42,103,435 = 42,103,435
and
-1 x -42,103,435 = 42,103,435
Notice both answers equal 42,103,435

With that explanation out of the way, let's continue. Next, we take the number 42,103,435 and divide it by 2:

42,103,435 ÷ 2 = 21,051,717.5

If the quotient is a whole number, then 2 and 21,051,717.5 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 42,103,435
-1 -42,103,435

Now, we try dividing 42,103,435 by 3:

42,103,435 ÷ 3 = 14,034,478.3333

If the quotient is a whole number, then 3 and 14,034,478.3333 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 42,103,435
-1 -42,103,435

Let's try dividing by 4:

42,103,435 ÷ 4 = 10,525,858.75

If the quotient is a whole number, then 4 and 10,525,858.75 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 42,103,435
-1 42,103,435
Keep dividing by the next highest number until you cannot divide anymore.

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

1511552391,1952,6293,20313,14516,01535,233176,165765,5173,827,5858,420,68742,103,435
-1-5-11-55-239-1,195-2,629-3,203-13,145-16,015-35,233-176,165-765,517-3,827,585-8,420,687-42,103,435

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