Q: What are the factor combinations of the number 46,140,605?

 A:
Positive:   1 x 461406055 x 92281217 x 659151535 x 131830347 x 98171549 x 941645235 x 196343245 x 188329329 x 1402451645 x 280492303 x 200354007 x 11515
Negative: -1 x -46140605-5 x -9228121-7 x -6591515-35 x -1318303-47 x -981715-49 x -941645-235 x -196343-245 x -188329-329 x -140245-1645 x -28049-2303 x -20035-4007 x -11515


How do I find the factor combinations of the number 46,140,605?

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 46,140,605, 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 46,140,605
-1 -46,140,605

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 46,140,605.

Example:
1 x 46,140,605 = 46,140,605
and
-1 x -46,140,605 = 46,140,605
Notice both answers equal 46,140,605

With that explanation out of the way, let's continue. Next, we take the number 46,140,605 and divide it by 2:

46,140,605 ÷ 2 = 23,070,302.5

If the quotient is a whole number, then 2 and 23,070,302.5 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 46,140,605
-1 -46,140,605

Now, we try dividing 46,140,605 by 3:

46,140,605 ÷ 3 = 15,380,201.6667

If the quotient is a whole number, then 3 and 15,380,201.6667 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 46,140,605
-1 -46,140,605

Let's try dividing by 4:

46,140,605 ÷ 4 = 11,535,151.25

If the quotient is a whole number, then 4 and 11,535,151.25 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 46,140,605
-1 46,140,605
Keep dividing by the next highest number until you cannot divide anymore.

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

1573547492352453291,6452,3034,00711,51520,03528,049140,245188,329196,343941,645981,7151,318,3036,591,5159,228,12146,140,605
-1-5-7-35-47-49-235-245-329-1,645-2,303-4,007-11,515-20,035-28,049-140,245-188,329-196,343-941,645-981,715-1,318,303-6,591,515-9,228,121-46,140,605

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