The number 734,851,474,594,578,436,096 is equal to n`^6` for some positive integer n. What is the value of n?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

734,851,474,594,578,436,096 = `3004^6`

The factorization of 734,851,474,594,578,436,096 is `2^(12)*751^6` or `4^6*751^6=3004^6`.

Since the number is even, we recognize it has a factor of 2. Dividing 2 out until we reach an odd number we get

4096*179,407,098,289,692,001.

We can then try a prime sieve to find the next factor to be 751. The result is also divisible by 751, and so on.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team