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Let N=1!⋅2!⋅3!⋅4!…9!⋅10!N = 1!\cdot 2! \cdot 3! \cdot 4! \ldots 9! \cdot 10!N=1!⋅2!⋅3!⋅4!…9!⋅10!. Let 2k2^k2k be the largest power of 222 that divides NNN. What is the value of kkk?
Details and assumptions
n!=n×(n−1)×(n−2)…2×1n! = n\times (n-1) \times (n-2) \ldots 2 \times 1n!=n×(n−1)×(n−2)…2×1.
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