Prime Numbers & Factors Class 6 Worksheet — Free PDF Download with Answers

A factor of a number divides it exactly without leaving a remainder. A prime number is a natural number greater than $1$ that has no factors other than $1$ and itself. Numbers with more than two factors are called composite numbers. The number $1$ is neither prime nor composite.

Prime numbers are the atoms of arithmetic — every whole number greater than $1$ can be expressed as a product of primes in exactly one way (up to order). This is called the Fundamental Theorem of Arithmetic, and while you will study it formally in higher classes, the Class 6 chapter on prime factorisation gives you a practical taste of it.

Understanding factors, multiples, HCF (Highest Common Factor), and LCM (Lowest Common Multiple) is essential not only for exams but for everyday problems like splitting items into equal groups, scheduling repeating events, and simplifying fractions.

* Factor — $a$ is a factor of $b$ if $b \div a$ leaves remainder $0$. E.g., factors of $12$: $1, 2, 3, 4, 6, 12$.
* Multiple — $b$ is a multiple of $a$ if $b = a \times k$ for some whole number $k$.
* Prime number — Has exactly two factors: $1$ and itself. First few primes: $2, 3, 5, 7, 11, 13, 17, 19, 23, 29$.
* Composite number — Has more than two factors. E.g., $4, 6, 8, 9, 10, \ldots$
* Prime factorisation — Writing a number as a product of primes. E.g., $60 = 2^2 \times 3 \times 5$.
* Factor tree method — Break a number into two factors, then break each non-prime factor further, until all leaves are prime.
* Division method — Divide by the smallest prime factor repeatedly until you reach $1$.
* HCF (Highest Common Factor) — The largest number that divides two or more numbers. Find by listing common prime factors with the lowest powers.
$\text{HCF}(12, 18) = 2 \times 3 = 6$.
* LCM (Lowest Common Multiple) — The smallest number that is a multiple of two or more numbers. Find by taking all prime factors with the highest powers.
$\text{LCM}(12, 18) = 2^2 \times 3^2 = 36$.
* Relation: $\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b$.

1. Print the PDF — Download from the links below.

2. Start with Level 1 (Easy) — 20 questions on identifying primes/composites, listing factors, and basic prime factorisation.

3. Time yourself — 15 minutes for Level 1, 20 for Level 2, 25 for Level 3.

4. Check answers — Use the included answer key.

5. Revise mistakes — For HCF/LCM errors, redo the prime factorisation from scratch.

6. Move to the next level — Progress when you score 16/20 or above.

Level 1 — Easy

1. Is $51$ prime or composite?
Solution: $51 = 3 \times 17$. Since it has factors other than $1$ and $51$, it is composite.

2. List all factors of $36$.
Solution: $1, 2, 3, 4, 6, 9, 12, 18, 36$.

3. Write the prime factorisation of $40$.
Solution: $40 = 2^3 \times 5$.

Level 2 — Medium

1. Find the HCF of $48$ and $72$.
Solution: $48 = 2^4 \times 3$ and $72 = 2^3 \times 3^2$. HCF $= 2^3 \times 3 = 24$.

2. Find the LCM of $15$ and $20$.
Solution: $15 = 3 \times 5$ and $20 = 2^2 \times 5$. LCM $= 2^2 \times 3 \times 5 = 60$.

3. Two alarm clocks ring every $8$ and $12$ minutes. If both ring at 9:00 AM, when do they next ring together?
Solution: LCM$(8, 12) = 24$. They ring together at 9:24 AM.

Level 3 — Hard

1. The HCF of two numbers is $12$ and their LCM is $180$. If one number is $36$, find the other.
Solution: $\text{HCF} \times \text{LCM} = a \times b \Rightarrow 12 \times 180 = 36 \times b \Rightarrow b = 60$.

2. Find the smallest number divisible by $12$, $15$, and $20$.
Solution: LCM$(12, 15, 20)$. $12 = 2^2 \times 3$, $15 = 3 \times 5$, $20 = 2^2 \times 5$. LCM $= 2^2 \times 3 \times 5 = 60$.

3. Prove that $2$ is the only even prime number.
Solution: Every even number $> 2$ is divisible by $2$, so it has at least three factors: $1$, $2$, and itself. Therefore no even number greater than $2$ can be prime. $2$ has exactly two factors ($1$ and $2$), so it is prime.

CBSE (NCERT — Ganita Prakash)
The "Prime Time" chapter covers prime and composite numbers, the Sieve of Eratosthenes, prime factorisation, and introduces HCF and LCM through factor trees. CBSE emphasises conceptual understanding and includes puzzles involving primes.

ICSE (Selina / ML Aggarwal)
The ICSE chapter is typically titled "HCF and LCM" and is more computation-heavy. Students are expected to find HCF and LCM of larger numbers and three-number sets. ICSE also tests the relationship $\text{HCF} \times \text{LCM} = a \times b$ in word problems.

IB MYP (Mathematics Framework)
The IB covers prime factorisation as part of the Number unit. Students investigate prime numbers through inquiry tasks and apply HCF/LCM to real-world scheduling and grouping problems. The emphasis is on reasoning and justification.

Key Differences:
* CBSE: Exploratory approach; Sieve of Eratosthenes; factor trees.
* ICSE: Computation-heavy; larger numbers; more word problems.
* IB: Inquiry-based; real-world applications; written justification.

Download your free Prime Numbers & Factors worksheets:

* Prime Time CBSE Worksheet — 60 questions aligned to NCERT
* HCF & LCM ICSE Worksheet — 60 questions aligned to Selina / ML Aggarwal

Practise online:

* Practice Online — CBSE
* Practice Online — ICSE

Each worksheet has 20 questions per level with a detailed answer key.

* AI Maths Solver — Stuck on an HCF/LCM problem? Get a step-by-step solution.
* Spark Coach — AI tutor that guides you with hints, not answers.
* Free Worksheets for All Classes — Browse worksheets from Class 1 to 10.
* Play Mode for Class 1-4 — Fun number games for younger learners.

Continue your Class 6 maths practice:

* Numbers & Place Value Class 6 Worksheet
* Whole Numbers Class 6 Worksheet
* Number Play Class 6 Worksheet
* Fractions & Decimals Class 6 Worksheet
* Ratio and Proportion Class 6 Worksheet