What is the lowest common factor?

The term "lowest common factor" is generally considered to be incorrect terminology. The correct term is greatest common factor (GCF), also known as the highest common factor (HCF).

Therefore, to answer what someone likely means when asking this question, we will explain the Greatest Common Factor (GCF).

Greatest Common Factor (GCF) Explained

The Greatest Common Factor (GCF), or Highest Common Factor (HCF), of two or more numbers is the largest positive integer that divides each of the numbers without leaving a remainder.

How to find the GCF:

Several methods exist to find the GCF. Two common methods are:

1. Listing Factors:

   • List all the factors of each number.
   • Identify the common factors (factors present in all lists).
   • The largest of these common factors is the GCF.

2. Prime Factorization:

   • Find the prime factorization of each number.
   • Identify the common prime factors.
   • Multiply the common prime factors raised to the lowest power they appear in any of the factorizations.

Example:

Let's find the GCF of 12 and 18 using both methods.

• Listing Factors:

  • Factors of 12: 1, 2, 3, 4, 6, 12
  • Factors of 18: 1, 2, 3, 6, 9, 18
  • Common Factors: 1, 2, 3, 6
  • GCF: 6

• Prime Factorization:

  • Prime factorization of 12: 2 x 2 x 3 = 2² x 3
  • Prime factorization of 18: 2 x 3 x 3 = 2 x 3²
  • Common Prime Factors: 2 and 3
  • GCF: 2¹ x 3¹ = 2 x 3 = 6

In both cases, the GCF of 12 and 18 is 6.

It is important to note the difference between GCF and LCM (Least Common Multiple). The reference mentions LCM (Least Common Multiple), which is the smallest positive integer that is divisible by both numbers.