HCF of 168 and 126 isa) 21b) 42c) 14d) 18

To find the Highest Common Factor (HCF) of 168 and 126, we can use the prime factorization method.

Step 1: Find the prime factorization of 168 168 ÷ 2 = 84 84 ÷ 2 = 42 42 ÷ 2 = 21 21 ÷ 3 = 7 7 ÷ 7 = 1

So, the prime factorization of 168 is: 168 = 2³ × 3 × 7

Step 2: Find the prime factorization of 126 126 ÷ 2 = 63 63 ÷ 3 = 21 21 ÷ 3 = 7 7 ÷ 7 = 1

So, the prime factorization of 126 is: 126 = 2 × 3² × 7

Step 3: Find the common prime factors and their lowest powers The common prime factors are 2, 3, and 7.

For 2, the lowest power is 2¹ (since 2³ and 2¹ are common).
For 3, the lowest power is 3¹ (since 3 and 3² are common).
For 7, the lowest power is 7¹.
Step 4: Multiply the common prime factors with their lowest powers: HCF = 2¹ × 3¹ × 7¹ = 2 × 3 × 7 = 42

So, the HCF of 168 and 126 is 42.

The correct answer is b) 42.