Q: What are the factor combinations of the number 42,053,683?

 A:
Positive:   1 x 420536837 x 600766923 x 182842129 x 1450127161 x 261203203 x 207161667 x 630494669 x 9007
Negative: -1 x -42053683-7 x -6007669-23 x -1828421-29 x -1450127-161 x -261203-203 x -207161-667 x -63049-4669 x -9007


How do I find the factor combinations of the number 42,053,683?

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 42,053,683, 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 42,053,683
-1 -42,053,683

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 42,053,683.

Example:
1 x 42,053,683 = 42,053,683
and
-1 x -42,053,683 = 42,053,683
Notice both answers equal 42,053,683

With that explanation out of the way, let's continue. Next, we take the number 42,053,683 and divide it by 2:

42,053,683 ÷ 2 = 21,026,841.5

If the quotient is a whole number, then 2 and 21,026,841.5 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 42,053,683
-1 -42,053,683

Now, we try dividing 42,053,683 by 3:

42,053,683 ÷ 3 = 14,017,894.3333

If the quotient is a whole number, then 3 and 14,017,894.3333 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 42,053,683
-1 -42,053,683

Let's try dividing by 4:

42,053,683 ÷ 4 = 10,513,420.75

If the quotient is a whole number, then 4 and 10,513,420.75 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 42,053,683
-1 42,053,683
Keep dividing by the next highest number until you cannot divide anymore.

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

1723291612036674,6699,00763,049207,161261,2031,450,1271,828,4216,007,66942,053,683
-1-7-23-29-161-203-667-4,669-9,007-63,049-207,161-261,203-1,450,127-1,828,421-6,007,669-42,053,683

More Examples

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