what-s-the-exponent-of-12-in-the-expansion-of-100-

Question Number 116113 by Lordose last updated on 01/Oct/20

{what}^{'} s the exponent of 12 in the

expansion of 100!

Answered by mr W last updated on 01/Oct/20

12 = 2^{2} \times 3

⌊ \frac{100}{2} ⌋ + ⌊ \frac{100}{2^{2}} ⌋ + ⌊ \frac{100}{2^{3}} ⌋ + \dots

= 50 + 25 + 12 + 6 + 3 + 1 = 97

⌊ \frac{100}{3} ⌋ + ⌊ \frac{100}{3^{2}} ⌋ + ⌊ \frac{100}{3^{3}} ⌋ + \dots

= 33 + 11 + 3 + 1 = 48

\Rightarrow 100! = 2^{97} \times 3^{48} \times \dots = 2 \times {(2^{2} \times 3)}^{48} \times \dots

= 12^{48} \times \dots

Commented by mr W last updated on 01/Oct/20

s e e a l s o Q 115294

Commented by bemath last updated on 01/Oct/20

sir help me qn 115988

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