Q: What are the factor combinations of the number 148,659,775?

 A:
Positive:   1 x 1486597755 x 2973195511 x 1351452525 x 594639155 x 270290597 x 1532575275 x 540581485 x 3065151067 x 1393252425 x 613035335 x 278655573 x 26675
Negative: -1 x -148659775-5 x -29731955-11 x -13514525-25 x -5946391-55 x -2702905-97 x -1532575-275 x -540581-485 x -306515-1067 x -139325-2425 x -61303-5335 x -27865-5573 x -26675


How do I find the factor combinations of the number 148,659,775?

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 148,659,775, 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.

1 148,659,775
-1 -148,659,775

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 148,659,775.

Example:
1 x 148,659,775 = 148,659,775
and
-1 x -148,659,775 = 148,659,775
Notice both answers equal 148,659,775

With that explanation out of the way, let's continue. Next, we take the number 148,659,775 and divide it by 2:

148,659,775 ÷ 2 = 74,329,887.5

If the quotient is a whole number, then 2 and 74,329,887.5 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:

1 148,659,775
-1 -148,659,775

Now, we try dividing 148,659,775 by 3:

148,659,775 ÷ 3 = 49,553,258.3333

If the quotient is a whole number, then 3 and 49,553,258.3333 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:

1 148,659,775
-1 -148,659,775

Let's try dividing by 4:

148,659,775 ÷ 4 = 37,164,943.75

If the quotient is a whole number, then 4 and 37,164,943.75 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:

1 148,659,775
-1 148,659,775
Keep dividing by the next highest number until you cannot divide anymore.

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

15112555972754851,0672,4255,3355,57326,67527,86561,303139,325306,515540,5811,532,5752,702,9055,946,39113,514,52529,731,955148,659,775
-1-5-11-25-55-97-275-485-1,067-2,425-5,335-5,573-26,675-27,865-61,303-139,325-306,515-540,581-1,532,575-2,702,905-5,946,391-13,514,525-29,731,955-148,659,775

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