GCF of 24 and 36

The Greatest Common Factor (GCF) of 24 and 36 is the highest number that can evenly divide both 24 and 36 without leaving a remainder. Understanding the concept of the GCF, also known as the Greatest Common Divisor (GCD), is essential in mathematics, especially in number theory and algebra. The factors of 24 include 1, 2, 3, 4, 6, 8, 12, and 24, while the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The GCF is a foundational concept that helps simplify fractions, solve equations, and understand relationships between numbers. To find the GCF of 24 and 36, three popular methods are used: the long division method, the prime factorization method, and the Euclidean algorithm.

GCF of 24 and 36

GCF of 24 and 36 is 12.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, while the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The Greatest Common Factor (GCF) of two non-zero integers, 24 and 36, is the largest positive integer, 12, that can divide both 24 and 36 without leaving a remainder.

Methods to Find GCF of 24 and 36

1. Prime Factorization Method
2. Long Division Method
3. Listing Common Factors

GCF of 24 and 36 by Prime Factorization Method

• Prime factorization of 24: 2 × 2 × 2 × 3
• Prime factorization of 36: 2 × 2 × 3 × 3
• Both 24 and 36 have common prime factors: 2 and 3
• The GCF is found by multiplying these common prime factors: 2 × 2 × 3 = 12
• Hence, the GCF of 24 and 36 is 12

GCF of 24 and 36 by Long Division Method

The long division method is a straightforward approach to find the Greatest Common Factor (GCF) of two numbers. Here are the steps to find the GCF of 24 and 36 using this method:

1. Divide the Larger Number by the Smaller Number:
   • Step 1: Divide 36 (larger number) by 24 (smaller number).
   • Result: The quotient is 1, and the remainder is 12.
   • 36÷24=136÷24=1 with a remainder of 12.
2. Replace the Larger Number with the Smaller Number:
   • Step 2: Now, replace the larger number (36) with the smaller number (24), and the smaller number (24) with the remainder from the previous division (12).
3. Repeat the Division Process:
   • Step 3: Divide 24 by 12.
   • Result: The quotient is 2, and the remainder is 0.
   • 24÷12=224÷12=2 with a remainder of 0.
4. Identify the GCF:
   • Step 4: Since the remainder is now 0, the divisor at this stage (12) is the GCF.
   • GCF: 12

GCF of 24 and 36 by Listing Common Factors

The numbers 24 and 36 share six common factors: 1, 2, 3, 4, 6, and 12. Among these, the largest common factor is 12. Therefore, the greatest common factor (GCF) of 24 and 36 is 12.