Q: What are the factor combinations of the number 67,017,115?

 A:
Positive:   1 x 670171155 x 1340342311 x 609246529 x 231093555 x 1218493145 x 462187319 x 2100851595 x 42017
Negative: -1 x -67017115-5 x -13403423-11 x -6092465-29 x -2310935-55 x -1218493-145 x -462187-319 x -210085-1595 x -42017


How do I find the factor combinations of the number 67,017,115?

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 67,017,115, 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 67,017,115
-1 -67,017,115

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 67,017,115.

Example:
1 x 67,017,115 = 67,017,115
and
-1 x -67,017,115 = 67,017,115
Notice both answers equal 67,017,115

With that explanation out of the way, let's continue. Next, we take the number 67,017,115 and divide it by 2:

67,017,115 ÷ 2 = 33,508,557.5

If the quotient is a whole number, then 2 and 33,508,557.5 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 67,017,115
-1 -67,017,115

Now, we try dividing 67,017,115 by 3:

67,017,115 ÷ 3 = 22,339,038.3333

If the quotient is a whole number, then 3 and 22,339,038.3333 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 67,017,115
-1 -67,017,115

Let's try dividing by 4:

67,017,115 ÷ 4 = 16,754,278.75

If the quotient is a whole number, then 4 and 16,754,278.75 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 67,017,115
-1 67,017,115
Keep dividing by the next highest number until you cannot divide anymore.

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

151129551453191,59542,017210,085462,1871,218,4932,310,9356,092,46513,403,42367,017,115
-1-5-11-29-55-145-319-1,595-42,017-210,085-462,187-1,218,493-2,310,935-6,092,465-13,403,423-67,017,115

More Examples

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