Q: What are the factor combinations of the number 35,132,335?

 A:
Positive:   1 x 351323355 x 70264677 x 501890535 x 1003781109 x 322315545 x 64463763 x 460453815 x 9209
Negative: -1 x -35132335-5 x -7026467-7 x -5018905-35 x -1003781-109 x -322315-545 x -64463-763 x -46045-3815 x -9209


How do I find the factor combinations of the number 35,132,335?

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 35,132,335, 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 35,132,335
-1 -35,132,335

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 35,132,335.

Example:
1 x 35,132,335 = 35,132,335
and
-1 x -35,132,335 = 35,132,335
Notice both answers equal 35,132,335

With that explanation out of the way, let's continue. Next, we take the number 35,132,335 and divide it by 2:

35,132,335 ÷ 2 = 17,566,167.5

If the quotient is a whole number, then 2 and 17,566,167.5 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 35,132,335
-1 -35,132,335

Now, we try dividing 35,132,335 by 3:

35,132,335 ÷ 3 = 11,710,778.3333

If the quotient is a whole number, then 3 and 11,710,778.3333 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 35,132,335
-1 -35,132,335

Let's try dividing by 4:

35,132,335 ÷ 4 = 8,783,083.75

If the quotient is a whole number, then 4 and 8,783,083.75 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 35,132,335
-1 35,132,335
Keep dividing by the next highest number until you cannot divide anymore.

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

157351095457633,8159,20946,04564,463322,3151,003,7815,018,9057,026,46735,132,335
-1-5-7-35-109-545-763-3,815-9,209-46,045-64,463-322,315-1,003,781-5,018,905-7,026,467-35,132,335

More Examples

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