Math CentralQuandaries & Queries


Question from pete, a student:

how do you find the number of factors in a really big number without using a factoring program or listing the out?


You can't. To find the factors and number of factors you really need to know the primes divide the number and how often. For example we know the number 25 x 37 x 138 has (5+1)(7+1)(8+1) = 432 divisors but it depends on knowing the primes appear to the exponents of 5, 7 and 8 respectively. To factor large numbers is extremely difficult, if not impossible, even for the world's fastest computers.



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