Q: What are the factor combinations of the number 71,537,521?

 A:
Positive:   1 x 7153752111 x 650341123 x 3110327157 x 455653253 x 2827571727 x 414231801 x 397213611 x 19811
Negative: -1 x -71537521-11 x -6503411-23 x -3110327-157 x -455653-253 x -282757-1727 x -41423-1801 x -39721-3611 x -19811


How do I find the factor combinations of the number 71,537,521?

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 71,537,521, 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 71,537,521
-1 -71,537,521

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 71,537,521.

Example:
1 x 71,537,521 = 71,537,521
and
-1 x -71,537,521 = 71,537,521
Notice both answers equal 71,537,521

With that explanation out of the way, let's continue. Next, we take the number 71,537,521 and divide it by 2:

71,537,521 ÷ 2 = 35,768,760.5

If the quotient is a whole number, then 2 and 35,768,760.5 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 71,537,521
-1 -71,537,521

Now, we try dividing 71,537,521 by 3:

71,537,521 ÷ 3 = 23,845,840.3333

If the quotient is a whole number, then 3 and 23,845,840.3333 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 71,537,521
-1 -71,537,521

Let's try dividing by 4:

71,537,521 ÷ 4 = 17,884,380.25

If the quotient is a whole number, then 4 and 17,884,380.25 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 71,537,521
-1 71,537,521
Keep dividing by the next highest number until you cannot divide anymore.

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

111231572531,7271,8013,61119,81139,72141,423282,757455,6533,110,3276,503,41171,537,521
-1-11-23-157-253-1,727-1,801-3,611-19,811-39,721-41,423-282,757-455,653-3,110,327-6,503,411-71,537,521

More Examples

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