Q: What are the factor combinations of the number 146,436,661?

 A:
Positive:   1 x 1464366617 x 2091952361 x 2400601241 x 607621427 x 3429431423 x 1029071687 x 868039961 x 14701
Negative: -1 x -146436661-7 x -20919523-61 x -2400601-241 x -607621-427 x -342943-1423 x -102907-1687 x -86803-9961 x -14701


How do I find the factor combinations of the number 146,436,661?

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 146,436,661, 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.

1 146,436,661
-1 -146,436,661

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 146,436,661.

Example:
1 x 146,436,661 = 146,436,661
and
-1 x -146,436,661 = 146,436,661
Notice both answers equal 146,436,661

With that explanation out of the way, let's continue. Next, we take the number 146,436,661 and divide it by 2:

146,436,661 ÷ 2 = 73,218,330.5

If the quotient is a whole number, then 2 and 73,218,330.5 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:

1 146,436,661
-1 -146,436,661

Now, we try dividing 146,436,661 by 3:

146,436,661 ÷ 3 = 48,812,220.3333

If the quotient is a whole number, then 3 and 48,812,220.3333 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:

1 146,436,661
-1 -146,436,661

Let's try dividing by 4:

146,436,661 ÷ 4 = 36,609,165.25

If the quotient is a whole number, then 4 and 36,609,165.25 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:

1 146,436,661
-1 146,436,661
Keep dividing by the next highest number until you cannot divide anymore.

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

17612414271,4231,6879,96114,70186,803102,907342,943607,6212,400,60120,919,523146,436,661
-1-7-61-241-427-1,423-1,687-9,961-14,701-86,803-102,907-342,943-607,621-2,400,601-20,919,523-146,436,661

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