If all the digits in a number are multiplied to form a new number in a iteration, then Multiplicative persistence, let P(n), is number of these iterations it takes for a number to reach single digit.
77 : 7*7 =49 : 36 : 18 : 8
4 iterations. Multiplicative Persistence 4.
But as there is option none. We should be sure there is no no., Between 27 and 77, with P(n) :4
Instead of brute forcing all iterations of these 50 digits. Think about this :
For P(n) > 1, the digit 0 doesn't occur and digit 1 doesn't occur and all terms have digits in nondecreasing order.
With little effort from above result you can be sure it is 77.
https://oeis.org/A003001
