Q: What are the factor combinations of the number 42,100,015?

 A:
Positive:   1 x 421000155 x 842000331 x 135806547 x 895745155 x 271613235 x 1791491457 x 288955779 x 7285
Negative: -1 x -42100015-5 x -8420003-31 x -1358065-47 x -895745-155 x -271613-235 x -179149-1457 x -28895-5779 x -7285


How do I find the factor combinations of the number 42,100,015?

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 42,100,015, 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 42,100,015
-1 -42,100,015

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 42,100,015.

Example:
1 x 42,100,015 = 42,100,015
and
-1 x -42,100,015 = 42,100,015
Notice both answers equal 42,100,015

With that explanation out of the way, let's continue. Next, we take the number 42,100,015 and divide it by 2:

42,100,015 ÷ 2 = 21,050,007.5

If the quotient is a whole number, then 2 and 21,050,007.5 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 42,100,015
-1 -42,100,015

Now, we try dividing 42,100,015 by 3:

42,100,015 ÷ 3 = 14,033,338.3333

If the quotient is a whole number, then 3 and 14,033,338.3333 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 42,100,015
-1 -42,100,015

Let's try dividing by 4:

42,100,015 ÷ 4 = 10,525,003.75

If the quotient is a whole number, then 4 and 10,525,003.75 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 42,100,015
-1 42,100,015
Keep dividing by the next highest number until you cannot divide anymore.

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

1531471552351,4575,7797,28528,895179,149271,613895,7451,358,0658,420,00342,100,015
-1-5-31-47-155-235-1,457-5,779-7,285-28,895-179,149-271,613-895,745-1,358,065-8,420,003-42,100,015

More Examples

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