HCF using product notation
for 8th grade

Find the highest common factor (HCF) of pairs of numbers using prime factorization and product notation

The highest common factor (HCF) of two numbers is the largest factor that is common to both numbers. It is also known as the Greatest Common Factor (GCF).

Product notation is a way of representing a number as a product of its prime factors. For example, the prime factorization of 24 can be written as 2³ × 3¹. To find the HCF of two or more numbers using product notation, you need to follow these steps:

1. Write the prime factorization of each number using product notation.
2. Identify the common factors of the two numbers
3. Take the lower power of each factor that appears in both of the factorizations.
4. Multiply the common factors together to get the HCF.

Example 1: Find the HCF of 18 and 24.

The prime factorization of 18 is:18 = 2¹ x 3²

The prime factorization of 24 is:24 = 2³ x 3¹

To find the HCF of 18 and 24, we take the lowest power of each prime factor that appears in both factorizations:

HCF(18,24) = 2¹ × 3¹ = 6

Example 2: Find the HCF of 16 and 28.

The prime factorization of 16 is:16 = 2⁴

The prime factorization of 28 is:28 = 2² x 7¹

To find the HCF of 16 and 28, we take the lower power of each prime factor that appears in both factorizations:

HCF(16,28) = 2² = 4

In this topic you are asked to find the highest common factor of pairs of numbers presenting your answers in product notation.