6 — Greatest Common Factor

Greatest Common Factor

Solution & Explanation · ID: EBFD0F19

Question

Use prime factorization to find the GCF of 48 and 72.

Hint

Break each number into prime factors, then use the lowest power of each common prime.

Concept

Prime factorization breaks numbers into their prime factors. To find the GCF, we multiply the common prime factors with their lowest powers.

Show Answer

24

Show Solution
1

Find prime factorization of 48: 48 = 2⁴ × 3¹

2

Find prime factorization of 72: 72 = 2³ × 3²

3

Identify common prime factors: 2 and 3

4

Take the lowest power of each common prime: 2³ and 3¹

5

Multiply: 2³ × 3¹ = 8 × 3 = 24

Prime factorization diagram showing 48 = 2⁴ × 3¹ and 72 = 2³ × 3². Common factors 2³ and 3¹ are highlighted. Below shows the calculation: GCF = 2³ × 3¹ = 8 × 3 = 24.