52 Factorial: How Many Zeros at the End?

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SUMMARY

The number of consecutive zeros at the end of 52! can be determined by calculating how many times 10 divides into 52!. This is equivalent to counting the pairs of factors 2 and 5 in the factorial's prime factorization. Since there are always more factors of 2 than 5, the count of factors of 5 will dictate the number of trailing zeros. For 52!, the number of trailing zeros is found by summing the integer divisions of 52 by powers of 5, resulting in a total of 10 trailing zeros.

PREREQUISITES
  • Understanding of factorial notation and calculations
  • Basic knowledge of prime factorization
  • Familiarity with integer division
  • Concept of trailing zeros in numbers
NEXT STEPS
  • Research the method for calculating trailing zeros in factorials
  • Learn about prime factorization techniques in number theory
  • Explore the concept of integer division and its applications
  • Investigate the properties of factorial growth and its implications
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Mathematicians, students studying combinatorics, educators teaching number theory, and anyone interested in understanding factorial properties and trailing zeros.

hypermonkey2
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how many consecutive zeros are at the end of 52! ?
 
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Try searching these forums, this well known type of question has been asked many times before.
 
yeah it isn't really as hard as it sounds, how many times does 10 divide 52!, that is, how many multiples of 2*5 can you count? you should be able to do it now.
 

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