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?

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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


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.

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