Q: What are the factor combinations of the number 1,506,155?

 A:
Positive:   1 x 15061555 x 3012317 x 21516523 x 6548535 x 43033115 x 13097161 x 9355805 x 1871
Negative: -1 x -1506155-5 x -301231-7 x -215165-23 x -65485-35 x -43033-115 x -13097-161 x -9355-805 x -1871


How do I find the factor combinations of the number 1,506,155?

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 1,506,155, 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 1,506,155
-1 -1,506,155

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 1,506,155.

Example:
1 x 1,506,155 = 1,506,155
and
-1 x -1,506,155 = 1,506,155
Notice both answers equal 1,506,155

With that explanation out of the way, let's continue. Next, we take the number 1,506,155 and divide it by 2:

1,506,155 ÷ 2 = 753,077.5

If the quotient is a whole number, then 2 and 753,077.5 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 1,506,155
-1 -1,506,155

Now, we try dividing 1,506,155 by 3:

1,506,155 ÷ 3 = 502,051.6667

If the quotient is a whole number, then 3 and 502,051.6667 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 1,506,155
-1 -1,506,155

Let's try dividing by 4:

1,506,155 ÷ 4 = 376,538.75

If the quotient is a whole number, then 4 and 376,538.75 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 1,506,155
-1 1,506,155
Keep dividing by the next highest number until you cannot divide anymore.

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

15723351151618051,8719,35513,09743,03365,485215,165301,2311,506,155
-1-5-7-23-35-115-161-805-1,871-9,355-13,097-43,033-65,485-215,165-301,231-1,506,155

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