Q: What are the factor combinations of the number 42,030,505?

 A:
Positive:   1 x 420305055 x 840610111 x 382095555 x 764191191 x 220055955 x 440112101 x 200054001 x 10505
Negative: -1 x -42030505-5 x -8406101-11 x -3820955-55 x -764191-191 x -220055-955 x -44011-2101 x -20005-4001 x -10505


How do I find the factor combinations of the number 42,030,505?

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 42,030,505, 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 42,030,505
-1 -42,030,505

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 42,030,505.

Example:
1 x 42,030,505 = 42,030,505
and
-1 x -42,030,505 = 42,030,505
Notice both answers equal 42,030,505

With that explanation out of the way, let's continue. Next, we take the number 42,030,505 and divide it by 2:

42,030,505 ÷ 2 = 21,015,252.5

If the quotient is a whole number, then 2 and 21,015,252.5 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 42,030,505
-1 -42,030,505

Now, we try dividing 42,030,505 by 3:

42,030,505 ÷ 3 = 14,010,168.3333

If the quotient is a whole number, then 3 and 14,010,168.3333 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 42,030,505
-1 -42,030,505

Let's try dividing by 4:

42,030,505 ÷ 4 = 10,507,626.25

If the quotient is a whole number, then 4 and 10,507,626.25 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 42,030,505
-1 42,030,505
Keep dividing by the next highest number until you cannot divide anymore.

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

1511551919552,1014,00110,50520,00544,011220,055764,1913,820,9558,406,10142,030,505
-1-5-11-55-191-955-2,101-4,001-10,505-20,005-44,011-220,055-764,191-3,820,955-8,406,101-42,030,505

More Examples

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