GCF of 15 and 20

The Greatest Common Factor (GCF) of 15 and 20 is the highest number that can evenly divide both 15 and 20 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 15 include 1, 3, 5, and 15, while the factors of 20 are 1, 2, 4, 5, 10, and 20. The GCF is a foundational concept that helps simplify fractions, solve equations, and understand relationships between numbers. To find the GCF of 15 and 20, three popular methods are used: the long division method, the prime factorization method, and the Euclidean algorithm.

GCF of 15 and 20

GCF of 15 and 20 is 5

The factors of 15 are 1, 3, 5, and 15, while the factors of 20 are 1, 2, 4, 5, 10, and 20. The Greatest Common Factor (GCF) of two non-zero integers, 15 and 20, is the largest positive integer, 5, that can divide both 15 and 20 without leaving a remainder.

Methods to Find GCF of 15 and 20

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

GCF of 15 and 20 by Prime Factorization Method

• Prime factorization of 15: 3 × 5
• Prime factorization of 20: 2 × 2 × 5
• Both 15 and 20 have a common prime factor: 5
• The GCF is found by multiplying this common prime factor: 5
• Hence, the GCF of 15 and 20 is 5.

GCF of 15 and 20 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 15 and 20 using this method:

Divide the Larger Number by the Smaller Number:

Step 1: Divide 20 (larger number) by 15 (smaller number).

Result: The quotient is 1, and the remainder is 5.

20÷15=120÷15=1 with a remainder of 5.

Replace the Larger Number with the Smaller Number:

Step 2: Now, replace the larger number (20) with the smaller number (15), and the smaller number (15) with the remainder from the previous division (5).

Repeat the Division Process:

Step 3: Divide 15 by 5.

Result: The quotient is 3, and the remainder is 0.

15÷5=315÷5=3 with a remainder of 0.

Identify the GCF:

Step 4: Since the remainder is now 0, the divisor at this stage (5) is the GCF.

GCF: 5

GCF of 15 and 20 by Listing Common Factors

The numbers 15 and 20 share two common factors: 1 and 5. Among these, the largest common factor is 5. Therefore, the greatest common factor (GCF) of 15 and 20 is 5.