Question
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Find the GCF (greatest common factor) of the following terms. \( \{21,85,22\} \)

Ask by Malone Fernandez. in the United States
Feb 27,2025

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Tutor-Verified Answer

Answer

The greatest common factor (GCF) of 21, 85, and 22 is 1.

Solution

To find the greatest common factor (GCF) of the set {21, 85, 22}, we need to determine if there is any number greater than 1 that divides all three numbers. Step 1: Factor each number. • 21 = 3 × 7 • 85 = 5 × 17 • 22 = 2 × 11 Step 2: Identify any common factors. Looking at the prime factors: • 21 has 3 and 7 • 85 has 5 and 17 • 22 has 2 and 11 There are no common factors among the three numbers. Since no number greater than 1 is common to all three, the greatest common factor is 1.

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The Deep Dive

To find the GCF of the numbers 21, 85, and 22, we begin by determining their prime factorizations. - The prime factorization of 21 is \(3 \times 7\). - The prime factorization of 85 is \(5 \times 17\). - The prime factorization of 22 is \(2 \times 11\). Since there are no common prime factors among all three numbers, it turns out that the GCF is 1. Now, let’s think about how this concept can apply in everyday situations! Whether you’re dividing up slices of pizza among friends or splitting a bill at a restaurant, understanding the GCF can help you evenly distribute items and avoid unnecessary leftovers. Also, for those who love getting the most out of their math skills, practicing GCF problems can improve your number sense and boost your problem-solving abilities. There are plenty of online resources, quizzes, and interactive games to make learning about divisors and multiples fun!

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