Q: What are the factor combinations of the number 1,398,145?

 A:
Positive:   1 x 13981455 x 2796297 x 19973535 x 3994743 x 32515215 x 6503301 x 4645929 x 1505
Negative: -1 x -1398145-5 x -279629-7 x -199735-35 x -39947-43 x -32515-215 x -6503-301 x -4645-929 x -1505


How do I find the factor combinations of the number 1,398,145?

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 1,398,145, 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 1,398,145
-1 -1,398,145

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 1,398,145.

Example:
1 x 1,398,145 = 1,398,145
and
-1 x -1,398,145 = 1,398,145
Notice both answers equal 1,398,145

With that explanation out of the way, let's continue. Next, we take the number 1,398,145 and divide it by 2:

1,398,145 ÷ 2 = 699,072.5

If the quotient is a whole number, then 2 and 699,072.5 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 1,398,145
-1 -1,398,145

Now, we try dividing 1,398,145 by 3:

1,398,145 ÷ 3 = 466,048.3333

If the quotient is a whole number, then 3 and 466,048.3333 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 1,398,145
-1 -1,398,145

Let's try dividing by 4:

1,398,145 ÷ 4 = 349,536.25

If the quotient is a whole number, then 4 and 349,536.25 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 1,398,145
-1 1,398,145
Keep dividing by the next highest number until you cannot divide anymore.

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

15735432153019291,5054,6456,50332,51539,947199,735279,6291,398,145
-1-5-7-35-43-215-301-929-1,505-4,645-6,503-32,515-39,947-199,735-279,629-1,398,145

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