Maharashtra Board Class 5 Maths Chapter 8 Multiples and Factors Set 34 Solutions

Question 1. Write all the prime numbers between 1 and 20.
Answer: 2, 3, 5, 7, 11, 13, 17, 19.
In simple words: Prime numbers between 1 and 20 are numbers greater than 1 that have only two factors: 1 and themselves. These are 2, 3, 5, 7, 11, 13, 17, and 19.

🎯 Exam Tip: Remember that 1 is neither prime nor composite. The number 2 is the only even prime number.

Question 2. Write all the composite numbers between 21 and 50.
Answer: Composite numbers between 21 and 50 are 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49.
In simple words: Composite numbers are whole numbers greater than 1 that have more than two factors. Between 21 and 50, these are all numbers except the prime numbers (23, 29, 31, 37, 41, 43, 47).

🎯 Exam Tip: To identify composite numbers, list numbers in the given range and eliminate prime numbers; the remaining numbers (excluding 1) will be composite.

Question 3. Circle the prime numbers in the list given below. 22, 37, 43, 48, 53, 60, 91, 57, 59, 77, 79, 97, 100
Answer: 22, 37, 43, 48, 53, 60, 91, 57, 59, 77 79, 97, 100, 81, 83, 67, 69, 41, 49, 31
In simple words: From the given list, the prime numbers are 37, 43, 53, 59, 79, 97, 83, 67, 41, and 31, as they are only divisible by 1 and themselves.

🎯 Exam Tip: Systematically test each number for divisibility by small prime numbers (2, 3, 5, 7, etc.) to confirm if it's prime or composite.

Question 4. Which of the prime numbers are even numbers?
Answer: Only even prime number is 2. (the Rest of the even numbers are composites.)
In simple words: The number 2 is unique because it is the only prime number that is also an even number; all other even numbers are divisible by 2, making them composite.

🎯 Exam Tip: Understanding the definition of prime (only two factors: 1 and itself) and even (divisible by 2) helps quickly identify 2 as the sole even prime number.

Co-Prime Numbers

Dada: Tell me all the factors of 12 and 18.

Anju: I'll tell the factors of 12: 1, 2, 3, 4, 6, 12.

Manju : I'll give the factors of 18: 1, 2, 3, 6, 9, 18.

Dada: Now find the common factors of 12 and 18.

Anju: Common factors ?

Dada : 1, 2, 3 and 6 are in both groups, which means that they are common factors. Now tell me the factors of 10 and 21.

Sanju: Factors of 10 : 1, 2, 5, 10.

Manju: Factors of 21: 1, 3, 7, 21.

Dada: Which of the factors in these two groups are common?

Sanju: 1 is the only common factor.

Dada : Numbers which have only 1 as a common factor are called co-prime numbers, so 10 and 21 are co-prime numbers. The common factors of 12 and 18 are 1, 2, 3 and 6; which means that the common factors are more than one. Therefore, 12 and 18 are not co-prime numbers. Now tell me whether 8 and 10 are co-prime numbers.

Manju: The factors of 8 are 1, 2, 4 and 8 and the factors of 10 are 1, 2, 5 and 10. These numbers have two factors, 1 and 2, in common, so 8 and 10 are not co-prime numbers.

Multiples And Factors Problem Set 32 Additional Important Questions And Answers

Question 1. 21 to 50
Answer: 23, 29, 31, 37, 41, 43, 47
In simple words: These are the prime numbers found within the range of 21 to 50, meaning they are only divisible by 1 and themselves.

🎯 Exam Tip: To quickly find primes in a range, use the Sieve of Eratosthenes or test for divisibility by small primes (2, 3, 5, 7, etc.).

Question 2. Which of the number is neither prime nor composite?
Answer: 1
In simple words: The number 1 is unique because it only has one factor (itself), which means it does not fit the definition of a prime number (two factors) or a composite number (more than two factors).

🎯 Exam Tip: Always remember the special case of the number 1 when classifying numbers as prime or composite.

Question 13. Between nearest which two prime numbers the prime number 43 lies?
Answer: 43 lies between prime numbers 41 and 47.
In simple words: To find the nearest prime numbers around 43, we look for prime numbers immediately before and after it, which are 41 and 47 respectively.

🎯 Exam Tip: Familiarize yourself with prime numbers up to a certain range (e.g., 100) to quickly identify neighboring primes.

Question 14. Which of the prime numbers are odd numbers?
Answer: All prime numbers are odd except 2.
In simple words: Except for the number 2, every other prime number is an odd number. This is because any even number greater than 2 is divisible by 2, making it composite.

🎯 Exam Tip: This is a fundamental concept: 2 is the only even prime number; all other primes are odd.