Class 6 Maths · Original EZT practice
Prime Time (Class 6 Chapter 5): summary and practice
Prime numbers are the building blocks every whole number is made from. This chapter goes through common multiples and common factors, primes and co-primes, prime factorisation, and quick divisibility tests. All questions are original EZT tutor practice following the chapter's own section order.
6 original worked examples, 6 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 22 October 2026:
1. Common multiples and common factors
A common multiple of two numbers is divisible by both; a common factor divides both. The smallest common multiple of 12 and 7 is 84, and the common factors of 12 and 18 are 1, 2, 3 and 6.
2. Prime numbers
A prime has exactly two factors: 1 and itself. 7 is prime, 12 is composite, and 1 is neither. The Sieve of Eratosthenes finds them all: keep 2, cross out its multiples, keep the next survivor, repeat.
3. Co-prime numbers
Two numbers are co-prime when 1 is their only common factor - like 12 and 25. Co-prime numbers need not be prime: 8 and 15 are co-prime and both composite.
4. Prime factorisation and divisibility tests
Every composite number splits into primes in exactly one way: 360 = 2^3 x 3^2 x 5. Divisibility tests skip the long division - digit sums for 3 and 9, last digits for 2, 5 and 10.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Smallest common multiple
Choose the method: Find the smallest number both divide exactly.
EZT practice question
Figs can be packed exactly in boxes of 12 or in boxes of 7. What is the smallest number of figs?
Show the worked solution
- We need the smallest common multiple of 12 and 7.
- Multiples of 12: 12, 24, 36, 48, 60, 72, 84.
- 84 = 12 x 7 is the first that 7 also divides.
Answer: 84 figs.
Check: 84 / 12 = 7 boxes and 84 / 7 = 12 boxes - both come out exact, and no smaller multiple of 12 is a multiple of 7.
Watch for this: A common multiple is not the product unless the numbers share no factor - here 12 x 7 = 84 works only because 12 and 7 are co-prime.
Now try it yourself
Smallest common multiple of 4 and 6?
Check your answer
12.
Multiples of 6: 6, 12 - 12 is the first divisible by 4.
List the common factors
Choose the method: List the factors of each number; the shared ones are common factors.
EZT practice question
Find the common factors of 12 and 18.
Show the worked solution
- Factors of 12: 1, 2, 3, 4, 6, 12.
- Factors of 18: 1, 2, 3, 6, 9, 18.
- Shared: 1, 2, 3, 6.
Answer: 1, 2, 3 and 6.
Check: Each of 1, 2, 3, 6 divides both 12 and 18 exactly - and the largest, 6, is their greatest common factor.
Watch for this: Do not skip 1 - it is a factor of every number and always a common factor.
Now try it yourself
Common factors of 24 and 36?
Check your answer
1, 2, 3, 4, 6, 12.
Both lists share exactly these.
Test for a prime
Choose the method: Count the factors: exactly two means prime.
EZT practice question
Is 2 a prime number? What is special about it?
Show the worked solution
- Factors of 2: 1 and 2 - exactly two.
- So 2 is prime.
- Every other even number has 2 as a factor, so no other even number can be prime.
Answer: Yes - 2 is the only even prime.
Check: The primes up to 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 - ten of them, and 2 is the only even one.
Watch for this: 1 is NOT prime - it has only one factor, so it is neither prime nor composite.
Now try it yourself
Is 15 prime?
Check your answer
No - factors 1, 3, 5, 15.
More than two factors makes it composite.
Check for co-prime numbers
Choose the method: If 1 is the only common factor, the pair is co-prime.
EZT practice question
Are 12 and 25 co-prime? Are 12 and 26?
Show the worked solution
- Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 25: 1, 5, 25.
- Only shared factor: 1 - so 12 and 25 are co-prime.
- But 12 and 26 share the factor 2 - not co-prime.
Answer: 12 and 25 are co-prime; 12 and 26 are not.
Check: Co-prime does not need prime: 8 and 15 are both composite yet co-prime, since 8 = 2^3 and 15 = 3 x 5 share nothing.
Watch for this: Do not assume two composite numbers cannot be co-prime - check the shared factors, not the labels.
Now try it yourself
Are 14 and 45 co-prime?
Check your answer
Yes.
14 = 2 x 7 and 45 = 3 x 3 x 5 share no prime factor.
Write the prime factorisation
Choose the method: Pull out prime factors one at a time until only primes remain.
EZT practice question
Write 360 as a product of primes.
Show the worked solution
- 360 = 2 x 180 = 2 x 2 x 90 = 2 x 2 x 2 x 45.
- 45 = 3 x 3 x 5.
- So 360 = 2^3 x 3^2 x 5.
Answer: 360 = 2^3 x 3^2 x 5.
Check: Multiply back: 8 x 9 x 5 = 360. And there is only one such factorisation - the order may change, the primes cannot.
Watch for this: Stop only when every factor is prime - 360 = 8 x 45 is a factorisation but not a PRIME factorisation.
Now try it yourself
Which is a product of exactly three distinct primes: 45 or 105?
Check your answer
105 = 3 x 5 x 7.
45 = 3 x 3 x 5 repeats a prime.
Use the divisibility tests
Choose the method: Digit sum for 3 and 9; last digit for 2, 5 and 10.
EZT practice question
Is 1242 divisible by 3 and by 9?
Show the worked solution
- Digit sum: 1 + 2 + 4 + 2 = 9.
- 9 is divisible by both 3 and 9.
- So 1242 is divisible by both - indeed 1242 = 9 x 138.
Answer: Yes, by both.
Check: The test works because 10, 100, 1000 all leave remainder 1 on division by 3 or 9 - only the digit sum carries the information.
Watch for this: The digit-sum test belongs to 3 and 9 - it says nothing about 2 or 5, which read the last digit.
Now try it yourself
Is 5730 divisible by 10, 5, 3 and 2?
Check your answer
Yes to all four.
Ends in 0 (10, 5, 2) and 5 + 7 + 3 + 0 = 15 is divisible by 3.
Try a mixed set
Choose a method or explanation before opening each answer.
1. Prime number?
Show answer and reason
Exactly two factors: 1 and itself.
7 is prime; 12 is not; 1 is neither.
2. Co-prime numbers?
Show answer and reason
Only common factor is 1.
Like 12 and 25 - primes not required.
3. Prime factorisation of 360?
Show answer and reason
2^3 x 3^2 x 5.
Every composite splits into primes one way.
4. Divisibility test for 9?
Show answer and reason
Digit sum divisible by 9.
1242 has digit sum 9 and equals 9 x 138.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Find all common factors of 24 and 36.
- Are 14 and 45 co-prime?
- Write 252 as a product of primes.
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Questions about this practice page
- What is a prime number?
- A number with exactly two factors - 1 and the number itself. 7 is prime and 12 is composite; 1 is neither prime nor composite because it has only one factor.
- What are co-prime numbers?
- Two numbers whose only common factor is 1, like 12 and 25. Co-prime numbers do not have to be prime themselves - 8 and 15 are both composite yet co-prime.
- What is prime factorisation?
- Writing a composite number as a product of primes, such as 360 = 2^3 x 3^2 x 5. Every composite number has exactly one prime factorisation, apart from the order of the factors.
- How does the divisibility test for 9 work?
- Add the digits of the number; if the sum is divisible by 9, the number is too. For 1242 the digit sum is 9, and indeed 1242 = 9 x 138.
- Are these the NCERT exercise questions for Prime Time (Class 6)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.