NCERT Solutions Class 6 Maths Chapter 5 Prime Time Exercise 5.4

In Chapter 5 - Prime Time, Exercise 5.4 will assist in getting you to understand the process of solving a range of puzzles and number problems that feature factors and multiples. The questions in Exercise 5.4 will help you understand prime numbers, HCF, LCM and  factorisation. 

The NCERT Solutions for all of the questions in Exercise 5.4 are developed from the latest CBSE and NCERT syllabus and written using a step-by-step process. 

The exercise will sharpen reasoning skills for the values discussed and see how mathematical concepts of numbers can be transferred to real-world situations. Working through and solving some of these types of questions can assist you in preparing for examinations and developing further confidence in mathematics. 

1.0Download NCERT Solutions Class 6 Maths Chapter 5 Prime Time Exercise 5.4: Free PDF

The NCERT Solutions for Class 6 Maths Chapter 5 help you understand factors and multiples. Get the free PDF of the solutions from below:

2.0NCERT Solutions Class 6 Chapter 5 Prime Time: All Exercises

3.0NCERT Class 6 Maths Chapter 5 Prime Time Exercise 5.4: Detailed Solutions

• Find the prime factorisations of the following numbers: $64,104,105,243,320,141,1728$, 729, 1024, 1331, 1000. Sol. (1) The prime factorisation of 64 is $2\times 2\times 2\times 2\times 2\times 2$. (2) The prime factorisation of 104 is $2\times 2\times 2\times 13$. (3) The prime factorisation of 105 is $3\times 5\times 7$. (4) The prime factorisation of 243 is $3\times 3\times 3\times 3\times 3$. (5) The prime factorisation of 320 is $2\times 2\times 2\times 2\times 2\times 2\times 5$. (6) The prime factorisation of 141 is $3\times 47$. (7) The prime factorisation of 1728 is $2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$. (8) The prime factorisation of 729 is $3\times 3\times 3\times 3\times 3\times 3$. (9) The prime factorisation of 1024 is $2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$. (10) The prime factorisation of 1331 is $11\times 11\times 11$. (11) The prime factorisation of 1000 is $2\times 2\times 2\times 5\times 5\times 5$.
• The prime factorisation of a number has one 2 , two 3 s , and one 11 . What is the number? Sol. To find the number, we multiply these prime factors together: $2\times 3\times 3\times 11=198$ Thus, the number is 198.
• Find three prime numbers, all less than 30 , whose product is 1955 . Sol. The prime factorisation of 1955: 1955 $=5\times 17\times 23$. All the factors are prime numbers and are less than 30 . Hence, the three prime numbers whose product is 1955 are 5, 17, and 23.
• Find the prime factorisation of these numbers without multiplying first. (a) $56\times 25$ (b) $108\times 75$ (c) $1000\times 81$ Sol. (a) Prime factors of $56=2\times 2\times 2\times 7$ Prime factors of $25=5\times 5$ Combined prime factorisation of $56\times 25=2\times 2\times 2\times 7\times 5\times 5$ (b) Prime factors of $108=2\times 2\times 3\times 3\times 3$ Prime factors of $75=3\times 5\times 5$ Combined prime factorisation of $108\times 75=2\times 2\times 3\times 3\times 3\times 3\times 5\times 5$ (c) Prime factors of $1000=2\times 2\times 2\times 5\times 5\times 5$ Prime factors of $81=3\times 3\times 3\times 3$ Combined prime factorisation of $1000\times 81=2\times 2\times 2\times 5\times 5\times 5\times 3\times 3\times 3\times 3$
• What is the smallest number whose prime factorisation has: (a) three different prime numbers? (b) four different prime numbers? Sol. (a) The smallest prime numbers are 2,3 , and 5 . To find the smallest number with these primes as factors, multiply them together: $2\times 3\times 5=30$. So, the smallest number whose prime factorisation has three different prime numbers is 30 . (b) The smallest four prime numbers are $2,3,5$, and 7 . To find the smallest number with these primes as factors, multiply them together: $2\times 3\times 5\times 7=210$. Thus, the smallest number whose prime factorisation has four different prime numbers is 210.
• Are the following pairs of numbers co-prime? Guess first and then use prime factorisation to verify your answer. (a) 30 and 45 (b) 57 and 85 (c) 121 and 1331 (d) 343 and 216 Sol. (a) Factors of 30 and 45: $\begin{array}{rl}& 30=2\times 3\times 5\\ & 45=3\times 3\times 5\end{array}$ Common factors: $3\times 5=15$. Hence, 30 and 45 are not a pair of co-prime numbers. (b) Factors of 57 and 85: $57=3\times 19$ $85=5\times 17$ No common factors other than 1 . Hence 57 and 85 are a pair of co-prime numbers. (c) Factors of 121 and 1331: $121=11\times 11$ $1331=11\times 11\times 11$ Common factors: $11\times 11=121$. Hence 121 and 1331 are not a pair of co-prime numbers. (d) Factors of 343 and 216: $343=7\times 7\times 7$ $216=2\times 2\times 2\times 3\times 3\times 3$ No common factors other than 1 . Hence 343 and 216 are a pair of co-prime numbers.
• Is the first number divisible by the second? Use prime factorisation. (a) 225 and 27 (b) 96 and 24 (c) 343 and 17 (d) 999 and 99 Sol. (a) Prime Factors of 225 and 27: $225=3\times 3\times 5\times 5$ and $27=3\times 3\times 3$ Since 225 contains $3\times 3$ and does not have enough factors of 3 to match $3\times 3\times 3,225$ does not have sufficient factors to be divisible by 27. Therefore, 225 is not divisible by 27. (b) Prime Factors of 96 and 24: $96=2\times 2\times 2\times 2\times 2\times 3$ and $24=2\times 2\times 2\times 3$ Since 96 includes the required factors to match those in 24 , it is divisible by 24 . (c) Prime Factors of 343 and 17: $343=7\times 7\times 7$ and $17=1\times 17$ Since the prime factorisation of 343 contains the prime factor 7 but not 17. Thus, 343 is not divisible by 17 . (d) Prime Factors of 999 and 99: $999=3\times 3\times 3\times 37$ and $99=3\times 3\times 11$ Since 999 does not include the factor 11, which is required for divisibility by 99 . Hence, 999 is not divisible by 99.
• The first number has prime factorisation $2\times 3\times 7$ and the second number has prime factorisation $3\times 7\times 11$. Are they co-prime? Does one of them divide the other? Sol. The numbers share the common factors 3 and 7. So they are not co-prime since neither number contains all the factors of the other, neither can divide the other.
• Guna says, "Any two prime numbers are co-prime". Is he right? Sol. Yes, Guna is right. Any two prime numbers are co-prime as they do not have common factor other than 1 which means they are always co-prime. For example, 2 and 3,5 and 7,11 and 13 .

4.0Key Features and benefits for Class 6 Maths Chapter 5 Exercise 5.4

• The exercise involves problems that involve concepts such as factors, multiples, and primes.
• The problems and questions follow the CBSE Class 6 Maths pattern and newest NCERT syllabus.
• Solving the NCERT Solutions will help improve critical thinking and problem solving skills for exams.
• These solutions can also help with preparation for olympiad exams by developing number sense and logic.