Q: What are the factor combinations of the number 42,012,553?

 A:
Positive:   1 x 4201255311 x 381932319 x 2211187179 x 234707209 x 2010171123 x 374111969 x 213373401 x 12353
Negative: -1 x -42012553-11 x -3819323-19 x -2211187-179 x -234707-209 x -201017-1123 x -37411-1969 x -21337-3401 x -12353


How do I find the factor combinations of the number 42,012,553?

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 42,012,553, 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 42,012,553
-1 -42,012,553

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 42,012,553.

Example:
1 x 42,012,553 = 42,012,553
and
-1 x -42,012,553 = 42,012,553
Notice both answers equal 42,012,553

With that explanation out of the way, let's continue. Next, we take the number 42,012,553 and divide it by 2:

42,012,553 ÷ 2 = 21,006,276.5

If the quotient is a whole number, then 2 and 21,006,276.5 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 42,012,553
-1 -42,012,553

Now, we try dividing 42,012,553 by 3:

42,012,553 ÷ 3 = 14,004,184.3333

If the quotient is a whole number, then 3 and 14,004,184.3333 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 42,012,553
-1 -42,012,553

Let's try dividing by 4:

42,012,553 ÷ 4 = 10,503,138.25

If the quotient is a whole number, then 4 and 10,503,138.25 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 42,012,553
-1 42,012,553
Keep dividing by the next highest number until you cannot divide anymore.

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

111191792091,1231,9693,40112,35321,33737,411201,017234,7072,211,1873,819,32342,012,553
-1-11-19-179-209-1,123-1,969-3,401-12,353-21,337-37,411-201,017-234,707-2,211,187-3,819,323-42,012,553

More Examples

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