CAT Exam  >  CAT Questions  >  How many natural numbers less than 200 are th... Start Learning for Free
How many natural numbers less than 200 are there such that (n-1)! is not divisible by n?
Most Upvoted Answer
How many natural numbers less than 200 are there such that (n-1)! is n...
Counting Natural Numbers



  • Definition: Natural numbers are whole numbers greater than zero. In other words, natural numbers are 1, 2, 3, 4, 5, and so on.

  • We want to count how many natural numbers less than 200 are such that (n-1)! is not divisible by n.



Solution



  • Prime Numbers: A natural number greater than 1 that has no positive divisors other than 1 and itself is called a prime number.

  • If n is a prime number, then (n-1)! is not divisible by n. There are 46 prime numbers less than 200.

  • Composite Numbers: A natural number that is not a prime number is called a composite number.

  • If n is a composite number, then (n-1)! is divisible by n.

  • Counting Composite Numbers: There are 153 composite numbers less than 200. We can count them by subtracting the number of prime numbers (46) from the total number of natural numbers less than 200 (199).

  • Total Count: Therefore, the total number of natural numbers less than 200 that satisfy the condition is 199 - 46 = 153.

Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
Explore Courses for CAT exam
How many natural numbers less than 200 are there such that (n-1)! is not divisible by n?
Question Description
How many natural numbers less than 200 are there such that (n-1)! is not divisible by n? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about How many natural numbers less than 200 are there such that (n-1)! is not divisible by n? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many natural numbers less than 200 are there such that (n-1)! is not divisible by n?.
Solutions for How many natural numbers less than 200 are there such that (n-1)! is not divisible by n? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of How many natural numbers less than 200 are there such that (n-1)! is not divisible by n? defined & explained in the simplest way possible. Besides giving the explanation of How many natural numbers less than 200 are there such that (n-1)! is not divisible by n?, a detailed solution for How many natural numbers less than 200 are there such that (n-1)! is not divisible by n? has been provided alongside types of How many natural numbers less than 200 are there such that (n-1)! is not divisible by n? theory, EduRev gives you an ample number of questions to practice How many natural numbers less than 200 are there such that (n-1)! is not divisible by n? tests, examples and also practice CAT tests.
Explore Courses for CAT exam

Top Courses for CAT

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev