Thank you for visiting Identify the greatest common divisor of the following pair of integers 22 times 33 times 55 and 25 times 32 times 52 A 110 B. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
To find the greatest common divisor of two sets of integers, prime factorize both numbers and identify common prime factors, choosing the minimum power of each common factor to determine the GCD. In this case, the GCD of the given pair of integers is 165. Therefore, option b) 165 is the correct answer.
Explanation:
The greatest common divisor of the integers 22 × 33 × 55 and 25 × 32 × 52 can be found by prime factorizing both numbers and then identifying the common prime factors.
- Prime factorization of 22 × 33 × 55 = 2 × 11 × 3 × 3 × 3 × 5 × 55
- Prime factorization of 25 × 32 × 52 = 5 × 5 × 3 × 3 × 2 × 2 × 5
- Identifying common prime factors and taking the minimum power gives us the greatest common divisor as 165.
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