Q: What are the factor combinations of the number 216,655,565?

 A:
Positive:   1 x 2166555655 x 433311137 x 3095079517 x 1274444535 x 619015985 x 2548889119 x 1820635595 x 364127
Negative: -1 x -216655565-5 x -43331113-7 x -30950795-17 x -12744445-35 x -6190159-85 x -2548889-119 x -1820635-595 x -364127


How do I find the factor combinations of the number 216,655,565?

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 216,655,565, 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.

1 216,655,565
-1 -216,655,565

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 216,655,565.

Example:
1 x 216,655,565 = 216,655,565
and
-1 x -216,655,565 = 216,655,565
Notice both answers equal 216,655,565

With that explanation out of the way, let's continue. Next, we take the number 216,655,565 and divide it by 2:

216,655,565 ÷ 2 = 108,327,782.5

If the quotient is a whole number, then 2 and 108,327,782.5 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:

1 216,655,565
-1 -216,655,565

Now, we try dividing 216,655,565 by 3:

216,655,565 ÷ 3 = 72,218,521.6667

If the quotient is a whole number, then 3 and 72,218,521.6667 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:

1 216,655,565
-1 -216,655,565

Let's try dividing by 4:

216,655,565 ÷ 4 = 54,163,891.25

If the quotient is a whole number, then 4 and 54,163,891.25 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:

1 216,655,565
-1 216,655,565
Keep dividing by the next highest number until you cannot divide anymore.

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

157173585119595364,1271,820,6352,548,8896,190,15912,744,44530,950,79543,331,113216,655,565
-1-5-7-17-35-85-119-595-364,127-1,820,635-2,548,889-6,190,159-12,744,445-30,950,795-43,331,113-216,655,565

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