Q: What are the factor combinations of the number 53,050,217?

 A:
Positive:   1 x 5305021711 x 482274717 x 3120601187 x 283691367 x 144551773 x 686294037 x 131416239 x 8503
Negative: -1 x -53050217-11 x -4822747-17 x -3120601-187 x -283691-367 x -144551-773 x -68629-4037 x -13141-6239 x -8503


How do I find the factor combinations of the number 53,050,217?

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 53,050,217, 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 53,050,217
-1 -53,050,217

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 53,050,217.

Example:
1 x 53,050,217 = 53,050,217
and
-1 x -53,050,217 = 53,050,217
Notice both answers equal 53,050,217

With that explanation out of the way, let's continue. Next, we take the number 53,050,217 and divide it by 2:

53,050,217 ÷ 2 = 26,525,108.5

If the quotient is a whole number, then 2 and 26,525,108.5 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 53,050,217
-1 -53,050,217

Now, we try dividing 53,050,217 by 3:

53,050,217 ÷ 3 = 17,683,405.6667

If the quotient is a whole number, then 3 and 17,683,405.6667 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 53,050,217
-1 -53,050,217

Let's try dividing by 4:

53,050,217 ÷ 4 = 13,262,554.25

If the quotient is a whole number, then 4 and 13,262,554.25 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 53,050,217
-1 53,050,217
Keep dividing by the next highest number until you cannot divide anymore.

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

111171873677734,0376,2398,50313,14168,629144,551283,6913,120,6014,822,74753,050,217
-1-11-17-187-367-773-4,037-6,239-8,503-13,141-68,629-144,551-283,691-3,120,601-4,822,747-53,050,217

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