Q: What are the factor combinations of the number 35,311,471?

 A:
Positive:   1 x 3531147113 x 271626743 x 821197181 x 195091349 x 101179559 x 631692353 x 150074537 x 7783
Negative: -1 x -35311471-13 x -2716267-43 x -821197-181 x -195091-349 x -101179-559 x -63169-2353 x -15007-4537 x -7783


How do I find the factor combinations of the number 35,311,471?

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 35,311,471, 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 35,311,471
-1 -35,311,471

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 35,311,471.

Example:
1 x 35,311,471 = 35,311,471
and
-1 x -35,311,471 = 35,311,471
Notice both answers equal 35,311,471

With that explanation out of the way, let's continue. Next, we take the number 35,311,471 and divide it by 2:

35,311,471 ÷ 2 = 17,655,735.5

If the quotient is a whole number, then 2 and 17,655,735.5 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 35,311,471
-1 -35,311,471

Now, we try dividing 35,311,471 by 3:

35,311,471 ÷ 3 = 11,770,490.3333

If the quotient is a whole number, then 3 and 11,770,490.3333 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 35,311,471
-1 -35,311,471

Let's try dividing by 4:

35,311,471 ÷ 4 = 8,827,867.75

If the quotient is a whole number, then 4 and 8,827,867.75 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 35,311,471
-1 35,311,471
Keep dividing by the next highest number until you cannot divide anymore.

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

113431813495592,3534,5377,78315,00763,169101,179195,091821,1972,716,26735,311,471
-1-13-43-181-349-559-2,353-4,537-7,783-15,007-63,169-101,179-195,091-821,197-2,716,267-35,311,471

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