Q: What are the factor combinations of the number 401,315,035?

 A:
Positive:   1 x 4013150355 x 8026300711 x 3648318555 x 729663761 x 6578935305 x 1315787671 x 5980853355 x 119617
Negative: -1 x -401315035-5 x -80263007-11 x -36483185-55 x -7296637-61 x -6578935-305 x -1315787-671 x -598085-3355 x -119617


How do I find the factor combinations of the number 401,315,035?

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 401,315,035, 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.

1 401,315,035
-1 -401,315,035

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 401,315,035.

Example:
1 x 401,315,035 = 401,315,035
and
-1 x -401,315,035 = 401,315,035
Notice both answers equal 401,315,035

With that explanation out of the way, let's continue. Next, we take the number 401,315,035 and divide it by 2:

401,315,035 ÷ 2 = 200,657,517.5

If the quotient is a whole number, then 2 and 200,657,517.5 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:

1 401,315,035
-1 -401,315,035

Now, we try dividing 401,315,035 by 3:

401,315,035 ÷ 3 = 133,771,678.3333

If the quotient is a whole number, then 3 and 133,771,678.3333 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:

1 401,315,035
-1 -401,315,035

Let's try dividing by 4:

401,315,035 ÷ 4 = 100,328,758.75

If the quotient is a whole number, then 4 and 100,328,758.75 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:

1 401,315,035
-1 401,315,035
Keep dividing by the next highest number until you cannot divide anymore.

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

151155613056713,355119,617598,0851,315,7876,578,9357,296,63736,483,18580,263,007401,315,035
-1-5-11-55-61-305-671-3,355-119,617-598,085-1,315,787-6,578,935-7,296,637-36,483,185-80,263,007-401,315,035

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