Discussion

Explanation:

21 = 3 × 7

Now, to calculate highest power of a prime number p in N!, we add all the quotients when N is successively divided by p.

So, highest power of 3 in 50! is:
Q(50/3) = 16
Q(16/3) = 5
Q(5/3) = 1
∴ Highest power of 3 in 50! = 16 + 5 + 1 = 22

So, highest power of 7 in 50! is:
Q(50/7) = 7
Q(7/7) = 1
∴ Highest power of 7 in 50! = 7 + 1 = 8

So when 50! is written in prime factorised form it will be:
⇒ 50! = 3²² × 7⁸ [There will be power of other prime numbers as well but that is immaterial for this question]
⇒ 50! = 3¹⁴ × 3⁸ × 7⁸ 
⇒ 50! = 3¹⁴ × (3 × 7)⁸
⇒ 50! = 3¹⁴ × 21⁸​​​​​​​

∴ Highest power of 21 in 50! is 8, hence 21⁸ can divided 50!.

Hence, option (c).

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