🧮 Class 10 Mathematics
Topic: Prime Factorisation
📘 What is Prime Factorisation?
Prime Factorisation is the process of expressing a number as a product of its prime factors. A prime number is a number that is divisible only by 1 and itself (e.g. 2, 3, 5, 7, 11...). Every number can be uniquely expressed as a product of primes — this is known as the Fundamental Theorem of Arithmetic.
💡 Example: The prime factorisation of 60 is: \[ 60 = 2 \times 2 \times 3 \times 5 = 2^2 \times 3 \times 5 \]
✏️ Solved Examples
1️⃣ Find the prime factorisation of 90:
\( 90 = 2 \times 3 \times 3 \times 5 = 2 \times 3^2 \times 5 \)
2️⃣ Prime factorise 84:
\( 84 = 2 \times 2 \times 3 \times 7 = 2^2 \times 3 \times 7 \)
3️⃣ Express 100 as a product of prime factors:
\( 100 = 2 \times 2 \times 5 \times 5 = 2^2 \times 5^2 \)
📚 Homework – Fully Solved Worksheet (1 Hour)
1️⃣ Prime factorise 72
Solution: \( 72 = 2 \times 2 \times 2 \times 3 \times 3 = 2^3 \times 3^2 \)
2️⃣ Prime factorisation of 126
Solution: \( 126 = 2 \times 3 \times 3 \times 7 = 2 \times 3^2 \times 7 \)
3️⃣ Express 150 as product of primes
Solution: \( 150 = 2 \times 3 \times 5 \times 5 = 2 \times 3 \times 5^2 \)
4️⃣ Prime factorisation of 144
Solution: \( 144 = 2^4 \times 3^2 \)
5️⃣ Prime factorise 180
Solution: \( 180 = 2^2 \times 3^2 \times 5 \)
6️⃣ Write the prime factorisation of 225
Solution: \( 225 = 3^2 \times 5^2 \)
7️⃣ Prime factorisation of 98
Solution: \( 98 = 2 \times 7 \times 7 = 2 \times 7^2 \)
8️⃣ Factorise 168
Solution: \( 168 = 2^3 \times 3 \times 7 \)
9️⃣ Express 256 as prime factors
Solution: \( 256 = 2^8 \)
🔟 Factorise 105 using primes
Solution: \( 105 = 3 \times 5 \times 7 \)