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What is the greatest common factor of 77 and \( 62 ? \)

Ask by Carlson Boyd. in the United States
Mar 13,2025

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Answer

The greatest common factor of 77 and 62 is 1.

Solution

1. Write each number as a product of its prime factors: - \(77 = 7 \times 11\) - \(62 = 2 \times 31\) 2. Identify the common prime factors: - There are no common prime factors between \(77\) and \(62\). 3. Since there are no common factors other than \(1\), the greatest common factor is: \[ \text{GCF} = 1 \]

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To find the greatest common factor of 77 and 62, we first need to factor each number. - The factors of 77 are 1, 7, 11, and 77. - The factors of 62 are 1, 2, 31, and 62. The largest number that appears in both lists is 1, making the greatest common factor of 77 and 62 equal to 1. Did you know that finding the greatest common factor is like looking for common ground in math? It helps us simplify fractions or solve problems where we need to distribute items evenly! When dealing with larger numbers, using the prime factorization method can be beneficial! Break down each number into its prime factors, and then multiply the smallest powers of the common primes to find the GCF. Enjoy the factor hunt!

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