Question

Using prime factorisation, find the HCF of 180, 140 and 210.

Hint:

List the prime factors of each number and take the product of the lowest powers of common factors.

Answer 1

Given:
Find HCF of 180, 140, and 210 using prime factorisation.

Step 1: Prime factorise each number
\[ 180 = 2^2 \times 3^2 \times 5 \] \[ 140 = 2^2 \times 5 \times 7 \] \[ 210 = 2 \times 3 \times 5 \times 7 \]

Step 2: Identify common prime factors with lowest powers
- Prime factor 2: lowest power is \(2^1\) (since 210 has only one 2)
- Prime factor 3: lowest power is \(3^0\) (140 does not have 3, so exclude)
- Prime factor 5: lowest power is \(5^1\)
- Prime factor 7: lowest power is \(7^0\) (180 does not have 7, so exclude)

Step 3: Calculate HCF
\[ \text{HCF} = 2^1 \times 5^1 = 2 \times 5 = 10 \]

Final Answer:
\[ \boxed{10} \]