Q: What are the factor combinations of the number 5,142,823?

 A:
Positive:   1 x 51428237 x 73468917 x 30251923 x 223601119 x 43217161 x 31943391 x 131531879 x 2737
Negative: -1 x -5142823-7 x -734689-17 x -302519-23 x -223601-119 x -43217-161 x -31943-391 x -13153-1879 x -2737


How do I find the factor combinations of the number 5,142,823?

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 5,142,823, 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 5,142,823
-1 -5,142,823

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 5,142,823.

Example:
1 x 5,142,823 = 5,142,823
and
-1 x -5,142,823 = 5,142,823
Notice both answers equal 5,142,823

With that explanation out of the way, let's continue. Next, we take the number 5,142,823 and divide it by 2:

5,142,823 ÷ 2 = 2,571,411.5

If the quotient is a whole number, then 2 and 2,571,411.5 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 5,142,823
-1 -5,142,823

Now, we try dividing 5,142,823 by 3:

5,142,823 ÷ 3 = 1,714,274.3333

If the quotient is a whole number, then 3 and 1,714,274.3333 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 5,142,823
-1 -5,142,823

Let's try dividing by 4:

5,142,823 ÷ 4 = 1,285,705.75

If the quotient is a whole number, then 4 and 1,285,705.75 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 5,142,823
-1 5,142,823
Keep dividing by the next highest number until you cannot divide anymore.

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

1717231191613911,8792,73713,15331,94343,217223,601302,519734,6895,142,823
-1-7-17-23-119-161-391-1,879-2,737-13,153-31,943-43,217-223,601-302,519-734,689-5,142,823

More Examples

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