Question

What is the Highest common factor of 60 and 468

Answer 1

The Highest Common Factor (HCF) of 60 and 468 is found by identifying the common prime factors and their lowest powers in both numbers, which are 2^2 and 3. Multiplying these yields the HCF of 12.

Step-by-step explanation:

The Highest Common Factor (HCF) of two numbers is the greatest number that divides both of them without leaving a remainder. To find the HCF of 60 and 468, we can use the prime factorization method. First, list the prime factors of each number:

• 60 = 2³ × 3 × 5
• 468 = 2² × 3² × 13

Next, identify the common prime factors and their lowest powers:

1. Both numbers have the prime factor 2. The lowest power of 2 that is common to both prime factorizations is 2².
2. Both numbers have the prime factor 3. The lowest power of 3 that is common to both prime factorizations is 3¹ (or just 3).

Now, multiply these common prime factors to get the HCF:

HCF = 2² × 3 = 4 × 3 = 12

Therefore, the Highest Common Factor of 60 and 468 is 12.