InterviewSolution
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InterviewSolution
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The number of zeros at the end of 100!, isA. 16B. 5C. 7D. 70 |
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Answer» We have, `70!""=2^(a)xx3^(b)xx5^(c)xx7^(d)xx.....` Now, `c=E_(2)(70!)=[(70)/(2)]+[(70)/(2^(2))]+[(70)/(2^(4))]+[(70)/(2^(5))]+[(70)/(2^(6))]` `impliesa=35+17+8+4+2+1=67` and, `c=E_(5)(70!)=[(70)/(2)]+[(70)/(5^(2))]=14+2=16` `:.70!""=2^(67)xx5^(16)xx3^(b)xx7^(d)xx......` `implies70!""=(2xx5)^(16)xx2^(51)xx3^(b)xx7^(d)xx......` `implies70!""=10^(16)xx2^(51)xx3^(b)xx7^(d)xx......` Thus, the number of zeros at the end of 70! is 16. |
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