Q: What are the factor combinations of the number 145,224,521?

 A:
Positive:   1 x 14522452113 x 1117111773 x 1989377137 x 1060033949 x 1530291117 x 1300131781 x 8154110001 x 14521
Negative: -1 x -145224521-13 x -11171117-73 x -1989377-137 x -1060033-949 x -153029-1117 x -130013-1781 x -81541-10001 x -14521


How do I find the factor combinations of the number 145,224,521?

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 145,224,521, 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.

1 145,224,521
-1 -145,224,521

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 145,224,521.

Example:
1 x 145,224,521 = 145,224,521
and
-1 x -145,224,521 = 145,224,521
Notice both answers equal 145,224,521

With that explanation out of the way, let's continue. Next, we take the number 145,224,521 and divide it by 2:

145,224,521 ÷ 2 = 72,612,260.5

If the quotient is a whole number, then 2 and 72,612,260.5 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:

1 145,224,521
-1 -145,224,521

Now, we try dividing 145,224,521 by 3:

145,224,521 ÷ 3 = 48,408,173.6667

If the quotient is a whole number, then 3 and 48,408,173.6667 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:

1 145,224,521
-1 -145,224,521

Let's try dividing by 4:

145,224,521 ÷ 4 = 36,306,130.25

If the quotient is a whole number, then 4 and 36,306,130.25 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:

1 145,224,521
-1 145,224,521
Keep dividing by the next highest number until you cannot divide anymore.

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

113731379491,1171,78110,00114,52181,541130,013153,0291,060,0331,989,37711,171,117145,224,521
-1-13-73-137-949-1,117-1,781-10,001-14,521-81,541-130,013-153,029-1,060,033-1,989,377-11,171,117-145,224,521

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