Q: What are the factor combinations of the number 146,263,523?

 A:
Positive:   1 x 1462635237 x 2089478941 x 356740379 x 1851437287 x 509629553 x 2644913239 x 451576451 x 22673
Negative: -1 x -146263523-7 x -20894789-41 x -3567403-79 x -1851437-287 x -509629-553 x -264491-3239 x -45157-6451 x -22673


How do I find the factor combinations of the number 146,263,523?

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 146,263,523, 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.

1 146,263,523
-1 -146,263,523

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 146,263,523.

Example:
1 x 146,263,523 = 146,263,523
and
-1 x -146,263,523 = 146,263,523
Notice both answers equal 146,263,523

With that explanation out of the way, let's continue. Next, we take the number 146,263,523 and divide it by 2:

146,263,523 ÷ 2 = 73,131,761.5

If the quotient is a whole number, then 2 and 73,131,761.5 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:

1 146,263,523
-1 -146,263,523

Now, we try dividing 146,263,523 by 3:

146,263,523 ÷ 3 = 48,754,507.6667

If the quotient is a whole number, then 3 and 48,754,507.6667 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:

1 146,263,523
-1 -146,263,523

Let's try dividing by 4:

146,263,523 ÷ 4 = 36,565,880.75

If the quotient is a whole number, then 4 and 36,565,880.75 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:

1 146,263,523
-1 146,263,523
Keep dividing by the next highest number until you cannot divide anymore.

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

1741792875533,2396,45122,67345,157264,491509,6291,851,4373,567,40320,894,789146,263,523
-1-7-41-79-287-553-3,239-6,451-22,673-45,157-264,491-509,629-1,851,437-3,567,403-20,894,789-146,263,523

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