Q: What are the factor combinations of the number 151,745?

 A:
Positive:   1 x 1517455 x 3034911 x 1379531 x 489555 x 275989 x 1705155 x 979341 x 445
Negative: -1 x -151745-5 x -30349-11 x -13795-31 x -4895-55 x -2759-89 x -1705-155 x -979-341 x -445


How do I find the factor combinations of the number 151,745?

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 151,745, 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.

1 151,745
-1 -151,745

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 151,745.

Example:
1 x 151,745 = 151,745
and
-1 x -151,745 = 151,745
Notice both answers equal 151,745

With that explanation out of the way, let's continue. Next, we take the number 151,745 and divide it by 2:

151,745 ÷ 2 = 75,872.5

If the quotient is a whole number, then 2 and 75,872.5 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:

1 151,745
-1 -151,745

Now, we try dividing 151,745 by 3:

151,745 ÷ 3 = 50,581.6667

If the quotient is a whole number, then 3 and 50,581.6667 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:

1 151,745
-1 -151,745

Let's try dividing by 4:

151,745 ÷ 4 = 37,936.25

If the quotient is a whole number, then 4 and 37,936.25 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:

1 151,745
-1 151,745
Keep dividing by the next highest number until you cannot divide anymore.

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

15113155891553414459791,7052,7594,89513,79530,349151,745
-1-5-11-31-55-89-155-341-445-979-1,705-2,759-4,895-13,795-30,349-151,745

More Examples

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