What is the greatest power of 143 which can divide 125! Exactly?
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5! has one 5 — > 5^1
so has 6!,7!,8! and 9!
But in case of 10!, there are two 5′s — > 5^2
therefore,
15! has 5^3, 20! has 5^4.
But again in case of 25!, it has 5^6 instead of 5^5 as the number 25 in 25! can be treated as 5x5.
There’s a shortcut to find this..
do prime factorization by 5 for the number factorial as you want to find greatest power of 5 that fits in. Add all the quotients. that gives you the answer.
so when I do prime factorization for 125 by 5, the answer is 25+5+1 = 31.
plz mark as brainlist if ihas correct
so has 6!,7!,8! and 9!
But in case of 10!, there are two 5′s — > 5^2
therefore,
15! has 5^3, 20! has 5^4.
But again in case of 25!, it has 5^6 instead of 5^5 as the number 25 in 25! can be treated as 5x5.
There’s a shortcut to find this..
do prime factorization by 5 for the number factorial as you want to find greatest power of 5 that fits in. Add all the quotients. that gives you the answer.
so when I do prime factorization for 125 by 5, the answer is 25+5+1 = 31.
plz mark as brainlist if ihas correct
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