Q: What are the factor combinations of the number 410,402,423?

 A:
Positive:   1 x 41040242317 x 2414131973 x 56219511241 x 330703
Negative: -1 x -410402423-17 x -24141319-73 x -5621951-1241 x -330703


How do I find the factor combinations of the number 410,402,423?

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 410,402,423, 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.

1 410,402,423
-1 -410,402,423

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 410,402,423.

Example:
1 x 410,402,423 = 410,402,423
and
-1 x -410,402,423 = 410,402,423
Notice both answers equal 410,402,423

With that explanation out of the way, let's continue. Next, we take the number 410,402,423 and divide it by 2:

410,402,423 ÷ 2 = 205,201,211.5

If the quotient is a whole number, then 2 and 205,201,211.5 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:

1 410,402,423
-1 -410,402,423

Now, we try dividing 410,402,423 by 3:

410,402,423 ÷ 3 = 136,800,807.6667

If the quotient is a whole number, then 3 and 136,800,807.6667 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:

1 410,402,423
-1 -410,402,423

Let's try dividing by 4:

410,402,423 ÷ 4 = 102,600,605.75

If the quotient is a whole number, then 4 and 102,600,605.75 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:

1 410,402,423
-1 410,402,423
Keep dividing by the next highest number until you cannot divide anymore.

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

117731,241330,7035,621,95124,141,319410,402,423
-1-17-73-1,241-330,703-5,621,951-24,141,319-410,402,423

More Examples

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