What is the gcf of 71 and 82

General
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what is the gcf of 71 and 82

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What is the GCF of 71 and 82?

Answer:

To find the greatest common factor (GCF) of 71 and 82, we need to identify the largest number that divides both of these numbers without leaving a remainder. The method to find the GCF involves a few steps:

Step 1: Understand Prime Factorization

Prime factorization involves writing down a number as a product of prime numbers. However, when dealing with smaller numbers such as 71 and 82, we often utilize different methods since these numbers themselves may be primes or have limited factors.

Step 2: Find Prime Factors of each Number

  • Prime factors of 71:

    • 71 is a prime number itself, and it’s greater than 1. So its only factors are 1 and 71.

  • Prime factors of 82:

    • The number 82 can be broken down into its prime factors.
    • 82 is an even number, so it is divisible by 2.
    • Dividing 82 by 2 gives us 41.
    • 41 is a prime number, meaning it can only be divided by 1 and 41.
    • Hence, the prime factorization of 82 is (2 \times 41).

Step 3: Compare Common Factors

  • Common factors of 71 and 82: List all the factors of each number and find the common ones.
    • Factors of 71: 1, 71
    • Factors of 82: 1, 2, 41, 82

The only common factor between these two sets is 1.

Step 4: Identifying the Greatest Common Factor

Since 1 is the only common factor,

  • The greatest common factor of 71 and 82 is simply 1.

Final Answer:

The greatest common factor (GCF) of 71 and 82 is 1.

This means that these two numbers are co-prime (or relatively prime) to each other. They do not have any shared divisors other than 1, highlighting the indivisible nature of 71 and the relatively prime nature of this pair of numbers.