What is the Highest Common Factor of 12, 36 and 240

To find the Highest Common Factor (HCF)—also known as the Greatest Common Divisor (GCD)—of 12, 36, and 240, we identify the largest number that divides all three numbers without leaving a remainder.

Step-by-Step Calculation (Prime Factorization Method)
Prime Factorize each number:

12 = 2 × 2 × 3 = 2² × 3¹

36 = 2 × 2 × 3 × 3 = 2² × 3²

240 = 2 × 2 × 2 × 2 × 3 × 5 = 2⁴ × 3¹ × 5¹

Identify common prime factors:
The common prime factors present in all three numbers are 2 and 3.

Select the lowest exponent for each common factor:

For the prime factor 2, the lowest exponent among 2², 2², and 2⁴ is 2².

For the prime factor 3, the lowest exponent among 3¹, 3², and 3¹ is 3¹.

Calculate the HCF:
HCF = 2² × 3¹ = 4 × 3 = 12