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if a(b!) is completely divisible by 5^11 where a is single digit number find the minimum value of b. |
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Answer» GIVEN : a(b!) is COMPLETELY divisible by 5^11 where a is single digit number To find : the minimum value of b. Solution: for minimum value of b a = 5 5.b! divisible by 5¹¹ => b! divisible by 5¹⁰ => [b/5] + [b/5²] + [b/5³] + ... + . ≥ 10 b = 5 => [5/5] + [5/5²] + [5/5³] + ... + . = 1 + 0 + = 1 b = 25 => [25/5] + [25/5²] + [25/5³] + ... + . = 5 + 1 + 0 + .. = 6 b = 50 => [50/5] + [50/5²] + [50/5³] + ... + . = 10 + 2 + 0 + .. = 12 b = 45 => [45/5] + [45/5²] + [45/5³] + ... + . = 9 + 1 + 0 + .. = 10 Hence minimum value of b = 45 Learn More: what is the highest power of 91 that divides 78! ? - Brainly.in the largest positive integer k such that 12^k divides (109)! is - Brainly.in |
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