Q: What are the factor combinations of the number 772,145?

 A:
Positive:   1 x 7721455 x 15442911 x 7019555 x 14039101 x 7645139 x 5555505 x 1529695 x 1111
Negative: -1 x -772145-5 x -154429-11 x -70195-55 x -14039-101 x -7645-139 x -5555-505 x -1529-695 x -1111


How do I find the factor combinations of the number 772,145?

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 772,145, 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.

1 772,145
-1 -772,145

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 772,145.

Example:
1 x 772,145 = 772,145
and
-1 x -772,145 = 772,145
Notice both answers equal 772,145

With that explanation out of the way, let's continue. Next, we take the number 772,145 and divide it by 2:

772,145 ÷ 2 = 386,072.5

If the quotient is a whole number, then 2 and 386,072.5 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:

1 772,145
-1 -772,145

Now, we try dividing 772,145 by 3:

772,145 ÷ 3 = 257,381.6667

If the quotient is a whole number, then 3 and 257,381.6667 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:

1 772,145
-1 -772,145

Let's try dividing by 4:

772,145 ÷ 4 = 193,036.25

If the quotient is a whole number, then 4 and 193,036.25 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:

1 772,145
-1 772,145
Keep dividing by the next highest number until you cannot divide anymore.

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

1511551011395056951,1111,5295,5557,64514,03970,195154,429772,145
-1-5-11-55-101-139-505-695-1,111-1,529-5,555-7,645-14,039-70,195-154,429-772,145

More Examples

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