Q: What are the factor combinations of the number 148,730,725?

 A:
Positive:   1 x 1487307255 x 2974614511 x 1352097513 x 1144082525 x 594922955 x 270419565 x 2288165143 x 1040075275 x 540839325 x 457633715 x 2080153575 x 41603
Negative: -1 x -148730725-5 x -29746145-11 x -13520975-13 x -11440825-25 x -5949229-55 x -2704195-65 x -2288165-143 x -1040075-275 x -540839-325 x -457633-715 x -208015-3575 x -41603


How do I find the factor combinations of the number 148,730,725?

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 148,730,725, 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.

1 148,730,725
-1 -148,730,725

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 148,730,725.

Example:
1 x 148,730,725 = 148,730,725
and
-1 x -148,730,725 = 148,730,725
Notice both answers equal 148,730,725

With that explanation out of the way, let's continue. Next, we take the number 148,730,725 and divide it by 2:

148,730,725 ÷ 2 = 74,365,362.5

If the quotient is a whole number, then 2 and 74,365,362.5 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:

1 148,730,725
-1 -148,730,725

Now, we try dividing 148,730,725 by 3:

148,730,725 ÷ 3 = 49,576,908.3333

If the quotient is a whole number, then 3 and 49,576,908.3333 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:

1 148,730,725
-1 -148,730,725

Let's try dividing by 4:

148,730,725 ÷ 4 = 37,182,681.25

If the quotient is a whole number, then 4 and 37,182,681.25 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:

1 148,730,725
-1 148,730,725
Keep dividing by the next highest number until you cannot divide anymore.

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

1511132555651432753257153,57541,603208,015457,633540,8391,040,0752,288,1652,704,1955,949,22911,440,82513,520,97529,746,145148,730,725
-1-5-11-13-25-55-65-143-275-325-715-3,575-41,603-208,015-457,633-540,839-1,040,075-2,288,165-2,704,195-5,949,229-11,440,825-13,520,975-29,746,145-148,730,725

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