Worksheet Solutions: Prime Time - 1 | Mathematics (Maths) Class 6 PDF Download

Multiple Choice Questions (MCQs)

Q1: Which of the following is a prime number?
(a) 49
(b) 51
(c) 53
(d) 55
Ans: (c) 53
Solution: 53 is a prime number as it has no divisors other than 1 and 53.

Q2: What is the first common multiple of 3 and 5?
(a) 10
(b) 12
(c) 15
(d) 20
Ans: (c) 15
Solution: The first common multiple of 3 and 5 is 15 because it is the smallest number that both 3 and 5 can divide into without a remainder.

Q3: How many prime numbers are there between 1 and 10?
(a) 2
(b) 3
(c) 4
(d) 5
Ans: (c) 4
Solution: The prime numbers between 1 and 10 are 2, 3, 5, and 7, making a total of 4.

Q4: Which pair of numbers is co-prime?
(a) 12 and 18
(b) 14 and 21
(c) 8 and 9
(d) 10 and 20
Ans: (c) 8 and 9
Solution: 8 and 9 are co-prime because they have no common factors other than 1.

Q5: The smallest number that is a multiple of both 3 and 4 is:
(a) 6
(b) 9
(c) 12
(d) 15
Ans: (c) 12
Solution: 12 is the smallest number that is a multiple of both 3 and 4 because it is the lowest common multiple of these two numbers.

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Fill in the Blanks

Q1: The smallest prime number is _____.
Ans: 2
Solution: The smallest prime number is 2, which is also the only even prime number. All other even numbers are composite.

Q2: Numbers that have only two factors, 1 and the number itself, are called _____.
Ans: Prime numbers
Solution: A prime number is a number that can only be divided evenly by 1 and itself, such as 3, 5, 7, etc.

Q3: The common multiples of 3 and 5 within the first 100 numbers are _____, _____, and _____.
Ans: 15, 30, 45
Solution: A common multiple of two numbers is a number that is a multiple of both. For 3 and 5, the common multiples include 15, 30, and 45.

Q4: The Sieve of _____ is a method used to find all prime numbers up to a certain number.
Ans: Eratosthenes
Solution: The Sieve of Eratosthenes is an ancient algorithm used to find all primes up to a specified integer by progressively marking the multiples of each prime starting from 2.

Q5: Numbers that are neither prime nor composite are _____.
Ans: 1
Solution: The number 1 is unique because it only has one factor, itself, and is thus neither prime nor composite.

Test: Prime Time - 1

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True or False

Q1: 9 is a prime number.
Ans: False
Solution: 9 is not a prime number because it can be divided by 1, 3, and 9.

Q2: The number 2 is the only even prime number.
Ans: True
Solution: 2 is the only even prime number because it can only be divided evenly by 1 and 2.

Q3: All multiples of 4 are also multiples of 2.
Ans: True
Solution: Every multiple of 4 is also a multiple of 2 because 4 is divisible by 2.

Q4: If a number is divisible by 8, it is also divisible by 4.
Ans: True
Solution: Since 8 is divisible by 4, any number divisible by 8 will also be divisible by 4.

Q5: The number 37 is a composite number.
Ans: False
Solution: 37 is a prime number as it only has two factors: 1 and 37.

Answer the following questions

Q1: List all the prime numbers between 10 and 20.
Ans: 11, 13, 17, 19
Solution: These numbers cannot be divided by any number other than 1 and themselves, making them prime.

Q2: Find the common factors of 24 and 36.
Ans: 1, 2, 3, 4, 6, 12
Solution: The common factors of 24 and 36 are the numbers that can divide both 24 and 36 without leaving a remainder.

Q3: What is the prime factorization of 72?
Ans: 2 × 2 × 2 × 3 × 3
Solution: The prime factorization of 72 involves breaking it down into its prime factors.

Q4: Identify two numbers between 1 and 50 that are co-prime.
Ans: 14 and 25
Solution: 14 and 25 are co-prime because they have no common factors other than 1.

Q5: What is the smallest multiple of 5 that is also a multiple of 3?
Ans: 15
Solution: 15 is the smallest number that is a multiple of both 5 and 3.

Q6.Is the first number divisible by the second? Use prime factorisation.

​a. 150 and 25

b. 84 and 12

Solution:

a. 150 and 25
Yes, 150 is divisible by 25.
Explanation: The prime factorization of 150 is 2 × 3 × 5 × 5, and the prime factorization of 25 is 5 × 5. Since 150 has all the factors of 25, it is divisible by 25.

b. 84 and 12
Yes, 84 is divisible by 12.
Explanation: The prime factorization of 84 is 2 × 2 × 3 × 7, and the prime factorization of 12 is 2 × 2 × 3. Since 84 has all the factors of 12, it is divisible by 12.

Q7: Find three prime numbers, all less than 50, whose product is 2310.

Solution: The prime factorization of 2310:
2310 = 2 × 3 × 5 × 7 × 11

Among these, select three prime numbers that are less than 50: 2, 3, and 5.

Hence, the three prime numbers whose product is 2310 are 2, 3, and 5.

Q8: What is the smallest number whose prime factorization has:

a. Three different prime numbers?

b. Four different prime numbers?

Solution:

a. The smallest prime numbers are 3, 5, and 7. To find the smallest number with these primes as factors, multiply them together:
3 × 5 × 7 = 105
So, the smallest number whose prime factorization has three different prime numbers is 105.

b. The smallest four prime numbers are 3, 5, 7, and 11. To find the smallest number with these primes as factors, multiply them together:
3 × 5 × 7 × 11 = 1155
Thus, the smallest number whose prime factorization has four different prime numbers is 1155.

Q9: Who am I?
 I am a number less than 50. One of my factors is 6. The sum of my digits is 9.

Solution: 6 is a factor of 6, 12, 18, 24, 30, 36, 42, 48, which are less than 50. Among these, the number whose digit sum is 9 is 36 (3 + 6 = 9).
So, I am 36.

Explanation: The number is 36 (since 3 + 6 = 9 and 36 is divisible by 6).

Q10. Which of the following numbers is the product of exactly three distinct prime numbers: 50, 84, 105, 280?

Solution:
Here,
50 = 2 × 5 × 5 (2 distinct primes)
84 = 2 × 2 × 3 × 7 (4 distinct primes)
105 = 3 × 5 × 7 (3 distinct primes)
280 = 2 × 2 × 2 × 5 × 7 (4 distinct primes)

Number 105 is the product of exactly three distinct prime numbers i.e. 3 × 5 × 7.