Q: What are the factor combinations of the number 35,616,625?

 A:
Positive:   1 x 356166255 x 712332511 x 323787525 x 142466555 x 647575125 x 284933275 x 1295151375 x 25903
Negative: -1 x -35616625-5 x -7123325-11 x -3237875-25 x -1424665-55 x -647575-125 x -284933-275 x -129515-1375 x -25903


How do I find the factor combinations of the number 35,616,625?

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 35,616,625, 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 35,616,625
-1 -35,616,625

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 35,616,625.

Example:
1 x 35,616,625 = 35,616,625
and
-1 x -35,616,625 = 35,616,625
Notice both answers equal 35,616,625

With that explanation out of the way, let's continue. Next, we take the number 35,616,625 and divide it by 2:

35,616,625 ÷ 2 = 17,808,312.5

If the quotient is a whole number, then 2 and 17,808,312.5 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 35,616,625
-1 -35,616,625

Now, we try dividing 35,616,625 by 3:

35,616,625 ÷ 3 = 11,872,208.3333

If the quotient is a whole number, then 3 and 11,872,208.3333 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 35,616,625
-1 -35,616,625

Let's try dividing by 4:

35,616,625 ÷ 4 = 8,904,156.25

If the quotient is a whole number, then 4 and 8,904,156.25 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 35,616,625
-1 35,616,625
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551252751,37525,903129,515284,933647,5751,424,6653,237,8757,123,32535,616,625
-1-5-11-25-55-125-275-1,375-25,903-129,515-284,933-647,575-1,424,665-3,237,875-7,123,325-35,616,625

More Examples

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