Answer:
2 × 3 × 25 = 150
Explanation:
To find the highest common factor (HCF) of 72, 150, and 300, we can use a variety of methods, such as prime factorization, listing factors, or the Euclidean algorithm. Here's one way to find the HCF using prime factorization:
First, we can factor each number into its prime factors:
72 = 2^3 × 3^2
150 = 2 × 3 × 5^2
300 = 2^2 × 3 × 5^2
Next, we can identify the common prime factors and their lowest exponents among the three numbers:
The prime factor 2 appears in all three numbers with an exponent of at least 1, so the HCF must contain 2^1 = 2.
The prime factor 3 appears in all three numbers with an exponent of at least 1, so the HCF must contain 3^1 = 3.
The prime factor 5 appears in all three numbers with an exponent of at least 2, so the HCF must contain 5^2 = 25.
Therefore, the HCF of 72, 150, and 300 is 2 × 3 × 25 = 150.