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Chapter Analysis
Beginner21 pages • EnglishQuick Summary
Chapter 5 of Class 6 Mathematics titled 'Prime Time' introduces students to the concept of prime numbers, prime factorization, and co-prime numbers. It explores methods to determine the divisibility of numbers by various factors, such as 10 and 5. The chapter also emphasizes the unique prime factorization of numbers and explains co-prime numbers through engaging puzzles and examples.
Key Topics
- •Understanding prime numbers
- •Exploring prime factorization
- •Concept of co-prime numbers
- •Divisibility rules and tests
- •Patterns in numbers
- •Using prime factorization to determine divisibility
Learning Objectives
- ✓Identify and define prime numbers
- ✓Perform prime factorization on composite numbers
- ✓Determine if two numbers are co-prime
- ✓Apply divisibility rules to solve mathematical problems
- ✓Recognize and describe patterns in number sequences
Questions in Chapter
Find numbers between 120 and 140 that are divisible by 8. Also find numbers between 1120 and 1140, and 3120 and 3140, that are divisible by 8. What do you observe?
Answer: The numbers between 120 & 140 divisible by 8 are = 128, 136. The numbers between 1120 & 1140 divisible by 8 are = 1128, 1136. The numbers between 3120 & 3140 divisible by 8 are = 3128, 3136.
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Change the last two digits of 8560 so that the resulting number is a multiple of 8.
Answer: 8552 is a multiple of 8.
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Consider this statement: 1. Only the last three digits matter when deciding if a given number is divisible by 8. 2. If the number formed by the last three digits is divisible by 8, then the original number is divisible by 8. 3. If the original number is divisible by 8, then the number formed by the last three digits is divisible by 8. Do you agree? Why or why not?
Answer: Yes, for all the statements.
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Additional Practice Questions
What is a prime number? Provide an example.
easyAnswer: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. An example is 7.
Explain the concept of prime factorization.
mediumAnswer: Prime factorization involves breaking down a composite number into the product of its prime factors. For example, the prime factorization of 84 is 2 × 2 × 3 × 7.
How can you determine if two numbers are co-prime?
mediumAnswer: Two numbers are co-prime if they have no common factors other than 1. This can be verified by checking if they share any prime factor.
List all prime numbers between 1 and 30.
easyAnswer: The prime numbers between 1 and 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Create a set of numbers that includes three twin primes.
mediumAnswer: The twin primes are pairs such as (3, 5), (11, 13), and (17, 19).