6 — Greatest Common Factor

Greatest Common Factor

Solution & Explanation · ID: 3B1EE7D8

Question

Find the GCF of 45, 60, and 75.

Hint

Use prime factorization for each number, then find the common prime factors with their lowest powers.

Concept

To find the GCF of three numbers using prime factorization, we find the prime factors of each number and multiply the common factors with their lowest powers.

Show Answer

15

Show Solution
1

Find prime factorization of 45: 45 = 3² × 5¹

2

Find prime factorization of 60: 60 = 2² × 3¹ × 5¹

3

Find prime factorization of 75: 75 = 3¹ × 5²

4

Identify common prime factors in all three: 3 and 5

5

Take the lowest power of each common prime: 3¹ and 5¹

6

Multiply: 3¹ × 5¹ = 3 × 5 = 15

Prime factorization diagram showing 45 = 3² × 5¹, 60 = 2² × 3¹ × 5¹, and 75 = 3¹ × 5². Common factors 3¹ and 5¹ are highlighted across all three numbers. Below shows the calculation: GCF = 3¹ × 5¹ = 3 × 5 = 15.