NCERT Solutions Class 6 Maths Chapter 5 Prime Time Exercise 5.5

Class 6 Maths NCERT Solutions Chapter 5 – Exercise 5.5 focuses on divisibility rules for 2, 4, 5, 8, and 10. Students solve leap year problems, analyse palindromes divisible by 4, determine remainders, classify statements as always/sometimes/never true, and apply logical shortcuts to check divisibility efficiently.

Access the complete NCERT Solutions by ALLEN experts for Class 6 Maths Chapter 5 Exercise 5.5 in the form of a free downloadable PDF. The solutions are written in an easy step-by-step process to ensue that the students understand the solutions for every problem in the exercise in great detail. Regular practice helps in better performance during the school assessments and final exams. They also help in improving analytical and problem skills

1.0Download NCERT Solutions Class 6 Maths Chapter 5 Prime Time Exercise 5.5: Free PDF

Exercise 5.5 is about prime factorisation and assists students in expressing any number as a product of prime numbers. This is essential in number theory and helps with concept clarity. Download the complete NCERT Solutions for Class 6 Maths Chapter 5 complete with free PDF from below:

2.0Key Concepts Covered in Exercise 5.5 Class 6 Maths

• Divisibility rules (2, 4, 5, 8, 10): Applying quick rules to determine whether a number is divisible by these numbers.
• Leap year concept (multiple of 4 rule): Understanding how divisibility by 4 relates to identifying leap years.
• Remainder calculation: Determining the remainder when numbers are divided by given divisors.
• Logical reasoning statements: Analysing mathematical statements to decide if they are always, sometimes, or never true.
• Palindromes and divisibility: Exploring how numbers that read the same forward and backward relate to divisibility properties.

3.0NCERT Solutions Class 6 Chapter 5 Prime Time: All Exercises

4.0NCERT Class 6 Maths Chapter 5 Prime Time Exercise 5.5: Detailed Solutions

• 2024 is a leap year (as February has 29 days). Leap years occur in the years that are multiples of 4, except for those years that are evenly divisible by 100 but not 400. (a) From the year you were born till now, which years were leap years? (b) From the year 2024 till 2099, how many leap years are there? Sol. Let the born year be 2010. (a) From the year 2010 till 2024, there are 4 leap years. 2012, 2016, 2020 and 2024. (b) The leap years from 2024 and 2099 are: 2024, 2028, 2032, 2036, 2040, 2044, 2048, 2052, 2056, 2060, 2064, 2068, 2072, 2076,2080, 2084, 2088, 2092, 2096. Hence, there are 19 leap years from 2024 till 2099.
• Find the largest and smallest 4 -digit numbers that are divisible by 4 and are also palindromes. Sol. Largest 4-digit number divisible by 4 and is also palindrome-8888. Smallest 4-digit number divisible by 4 and is also palindrome-2112.
• Explore and find out if each statement is always true, sometimes true or never true. You can give examples to support your reasoning. (a) Sum of two even numbers gives a multiple of 4. (b) Sum of two odd numbers gives a multiple of 4. Sol. (a) Sometimes true. Sum of any two even numbers is not always divisible by 4. For example, $6+4=10$ which is not divisible by 4 whereas $2+2=4$ which is divisible by 4 . (b) Sometimes true. Sum of two odd numbers can indeed be even but not necessarily a multiple of 4 . For example, $1+5=6$ which is not a multiple of 4 whereas $1+3=4$, which is a multiple of 4 . Similarly, $7+5=12$, which is a multiple of 4 .
• Find the remainders obtained when each of the following numbers are divided by (i) 10 (ii) 5 (iii) 2. 78, 99, 173, 572, 980, 1111, 2345 Sol. Here we have to divide 78 by 10, 5 and 2 then
  

• The teacher asked if 14560 is divisible by all of $2,4,5,8$ and 10 . Guna checked for divisibility of 14560 by only two of these numbers and then declared that it was also divisible by all of them. What could those two numbers be? Sol. If a number is divisible by 8 , it will automatically be divisible by 4 . If a number is divisible by 10, it is also divisible by 2 and 5 . Therefore, checking divisibility by 8 and 10 confirms divisibility by all other numbers $(2,4,5)$. Thus, the pair of numbers that Guna could check to determine that 14560 is divisible by all of $2,4,5,8$, and 10 is: 8 and 10 .
• Which of the following numbers are divisible by all of $2,4,5,8$ and $10:572,2352,5600$, 6000, 77622160? Sol. Check for numbers which are divisible by 8 and 10 . $5600,6000,77622160$ are the numbers divisible by $2,4,5,8,10$.
• Write two numbers whose product is 10000 . The two numbers should not have 0 as the units digit. Sol. We need to write factors of 10000 . $10000=10\times 10\times 10\times 10=2\times 5\times 2\times 5\times 2\times 5\times 2\times 5$ So, $2\times 2\times 2\times 2=16$ and $5\times 5\times 5\times 5=625$. Hence, 16 and 625 are the two numbers whose product is 10000 .

5.0Key Features and benefits for Class 6 Maths Chapter 5 Exercise 5.5

• The questions in the exercise focuses on prime factorisation and they comprise 'division' and 'factor' trees. 
• It also follows the latest NCERT syllabus laid out for Class 6 Maths, by CBSE. 
• Solving NCERT solutions improves your accuracy and confidence at solving problems connected to numbers.
• Working through the questions helps you to perform better in your school maths exams and preparation for the Maths Olympiada. 
• Regular practice with the solutions allows learning to take place step-by-step, and can be useful during exam preparations