Find the highest power of 24 in 50!?
Explanation:
24 = 23 × 3
∴ Highest power of 2 in 50! = 502+5022+5023+5024+5025 = 25 + 12 + 6 + 3 + 1 = 47.
⇒ Highest power of 23 (i.e., 8) in 50! = 15.
∴ Highest power of 3 in 50! = 503+5032+5033 = 16 + 5 + 1 = 22.
Hence, 50! = (8)15 × 322 × k (k is an integer and does not contain any power of 2 or 3)
⇒ 50! = (24)15 × 37 × k
∴ Highest power of 24 in 50! Is 15.
Hence, 15.
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