Q: What are the factor combinations of the number 46,406,311?

 A:
Positive:   1 x 464063117 x 662947317 x 2729783119 x 389969271 x 1712411439 x 322491897 x 244634607 x 10073
Negative: -1 x -46406311-7 x -6629473-17 x -2729783-119 x -389969-271 x -171241-1439 x -32249-1897 x -24463-4607 x -10073


How do I find the factor combinations of the number 46,406,311?

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 46,406,311, 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 46,406,311
-1 -46,406,311

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 46,406,311.

Example:
1 x 46,406,311 = 46,406,311
and
-1 x -46,406,311 = 46,406,311
Notice both answers equal 46,406,311

With that explanation out of the way, let's continue. Next, we take the number 46,406,311 and divide it by 2:

46,406,311 ÷ 2 = 23,203,155.5

If the quotient is a whole number, then 2 and 23,203,155.5 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 46,406,311
-1 -46,406,311

Now, we try dividing 46,406,311 by 3:

46,406,311 ÷ 3 = 15,468,770.3333

If the quotient is a whole number, then 3 and 15,468,770.3333 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 46,406,311
-1 -46,406,311

Let's try dividing by 4:

46,406,311 ÷ 4 = 11,601,577.75

If the quotient is a whole number, then 4 and 11,601,577.75 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 46,406,311
-1 46,406,311
Keep dividing by the next highest number until you cannot divide anymore.

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

17171192711,4391,8974,60710,07324,46332,249171,241389,9692,729,7836,629,47346,406,311
-1-7-17-119-271-1,439-1,897-4,607-10,073-24,463-32,249-171,241-389,969-2,729,783-6,629,473-46,406,311

More Examples

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