Q: What are the factor combinations of the number 4,731,965?

 A:
Positive:   1 x 47319655 x 9463937 x 67599535 x 135199353 x 13405383 x 123551765 x 26811915 x 2471
Negative: -1 x -4731965-5 x -946393-7 x -675995-35 x -135199-353 x -13405-383 x -12355-1765 x -2681-1915 x -2471


How do I find the factor combinations of the number 4,731,965?

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 4,731,965, 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 4,731,965
-1 -4,731,965

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 4,731,965.

Example:
1 x 4,731,965 = 4,731,965
and
-1 x -4,731,965 = 4,731,965
Notice both answers equal 4,731,965

With that explanation out of the way, let's continue. Next, we take the number 4,731,965 and divide it by 2:

4,731,965 ÷ 2 = 2,365,982.5

If the quotient is a whole number, then 2 and 2,365,982.5 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 4,731,965
-1 -4,731,965

Now, we try dividing 4,731,965 by 3:

4,731,965 ÷ 3 = 1,577,321.6667

If the quotient is a whole number, then 3 and 1,577,321.6667 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 4,731,965
-1 -4,731,965

Let's try dividing by 4:

4,731,965 ÷ 4 = 1,182,991.25

If the quotient is a whole number, then 4 and 1,182,991.25 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 4,731,965
-1 4,731,965
Keep dividing by the next highest number until you cannot divide anymore.

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

157353533831,7651,9152,4712,68112,35513,405135,199675,995946,3934,731,965
-1-5-7-35-353-383-1,765-1,915-2,471-2,681-12,355-13,405-135,199-675,995-946,393-4,731,965

More Examples

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