Q: What are the factor combinations of the number 42,110,233?

 A:
Positive:   1 x 4211023311 x 382820329 x 1452077101 x 416933319 x 1320071111 x 379031307 x 322192929 x 14377
Negative: -1 x -42110233-11 x -3828203-29 x -1452077-101 x -416933-319 x -132007-1111 x -37903-1307 x -32219-2929 x -14377


How do I find the factor combinations of the number 42,110,233?

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 42,110,233, 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 42,110,233
-1 -42,110,233

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 42,110,233.

Example:
1 x 42,110,233 = 42,110,233
and
-1 x -42,110,233 = 42,110,233
Notice both answers equal 42,110,233

With that explanation out of the way, let's continue. Next, we take the number 42,110,233 and divide it by 2:

42,110,233 ÷ 2 = 21,055,116.5

If the quotient is a whole number, then 2 and 21,055,116.5 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 42,110,233
-1 -42,110,233

Now, we try dividing 42,110,233 by 3:

42,110,233 ÷ 3 = 14,036,744.3333

If the quotient is a whole number, then 3 and 14,036,744.3333 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 42,110,233
-1 -42,110,233

Let's try dividing by 4:

42,110,233 ÷ 4 = 10,527,558.25

If the quotient is a whole number, then 4 and 10,527,558.25 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 42,110,233
-1 42,110,233
Keep dividing by the next highest number until you cannot divide anymore.

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

111291013191,1111,3072,92914,37732,21937,903132,007416,9331,452,0773,828,20342,110,233
-1-11-29-101-319-1,111-1,307-2,929-14,377-32,219-37,903-132,007-416,933-1,452,077-3,828,203-42,110,233

More Examples

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