Multiple choice general knowledge

Find the greatest power of two which can exactly divides 150!

  1. 144

  2. 145

  3. 146

  4. 147

  5. 150
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Use Legendre's formula: exponent of prime p in n! = floor(n/p) + floor(n/p²) + floor(n/p³) + ... For 150! and p=2: floor(150/2)=75, floor(150/4)=37, floor(150/8)=18, floor(150/16)=9, floor(150/32)=4, floor(150/64)=2, floor(150/128)=1. Sum = 146.

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