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AMC 8 2026 (Problem 24)

The factorial notation n!n! is defined as the product of the first nn positive integers. (For example, 3!=1⋅2⋅3=63!=1\cdot2\cdot3=6.) Define the superfactorial of a positive number, denoted by n!n^{!}, to be the product of the factorials of the first nn integers. (For example, 3!=1!⋅2!⋅3!=123^{!}=1!\cdot2!\cdot3!=12.) How many factors of 7 appear in the prime factorization of 51!51^{!}, the superfactorial of 51?
(A)  147\text{(A)}\;147(B)  150\text{(B)}\;150(C)  156\text{(C)}\;156(D)  168\text{(D)}\;168(E)  171\text{(E)}\;171