Q: What are the factor combinations of the number 401,734,345?

 A:
Positive:   1 x 4017343455 x 8034686937 x 1085768567 x 5996035185 x 2171537335 x 11992072479 x 16205512395 x 32411
Negative: -1 x -401734345-5 x -80346869-37 x -10857685-67 x -5996035-185 x -2171537-335 x -1199207-2479 x -162055-12395 x -32411


How do I find the factor combinations of the number 401,734,345?

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 401,734,345, 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.

1 401,734,345
-1 -401,734,345

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 401,734,345.

Example:
1 x 401,734,345 = 401,734,345
and
-1 x -401,734,345 = 401,734,345
Notice both answers equal 401,734,345

With that explanation out of the way, let's continue. Next, we take the number 401,734,345 and divide it by 2:

401,734,345 ÷ 2 = 200,867,172.5

If the quotient is a whole number, then 2 and 200,867,172.5 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:

1 401,734,345
-1 -401,734,345

Now, we try dividing 401,734,345 by 3:

401,734,345 ÷ 3 = 133,911,448.3333

If the quotient is a whole number, then 3 and 133,911,448.3333 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:

1 401,734,345
-1 -401,734,345

Let's try dividing by 4:

401,734,345 ÷ 4 = 100,433,586.25

If the quotient is a whole number, then 4 and 100,433,586.25 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:

1 401,734,345
-1 401,734,345
Keep dividing by the next highest number until you cannot divide anymore.

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

1537671853352,47912,39532,411162,0551,199,2072,171,5375,996,03510,857,68580,346,869401,734,345
-1-5-37-67-185-335-2,479-12,395-32,411-162,055-1,199,207-2,171,537-5,996,035-10,857,685-80,346,869-401,734,345

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