Greatest Common Factor of 77 and 82

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

• Greatest Common Factor of 77 and 82 by prime factorization method
• Greatest Common Factor of 77 and 82 by matching factors method

Prime Factorization of 77

Prime factors of 77 are 7,11. Prime factorization of 77 in exponential form is:

77 = 7¹×11¹

Prime Factorization of 82

Prime factors of 82 are 2,41. Prime factorization of 82 in exponential form is:

82 = 2¹×41¹

∴ So by taking common prime factors GCF of 77 and 82 is 1

Factors of 77

List of positive integer factors of 77 that divides 77 without a remainder.

1,7,11,77

Factors of 82

List of positive integer factors of 82 that divides 82 without a remainder.

1,2,41,82

Greatest Common Factor

We found the factors and prime factorization of 77 and 82. The biggest common factor number is the GCF number.
So the greatest common factor 77 and 82 is 1.

Also check out the Least Common Multiple of 77 and 82

(i) The GCF of 77 and 82 is associative

GCF of 77 and 82 = GCF of 82 and 77

1. What is the GCF of 77 and 82?

Answer: GCF of 77 and 82 is 1.

2. What are the Factors of 77?

Answer: Factors of 77 are 1, 7, 11, 77. There are 4 integers that are factors of 77. The greatest factor of 77 is 77.

3. What are the Factors of 82?

Answer: Factors of 82 are 1, 2, 41, 82. There are 4 integers that are factors of 82. The greatest factor of 82 is 82.

4. How to Find the GCF of 77 and 82?

Answer:

Greatest Common Factor of 77 and 82 = 1

Step 1: Find the prime factorization of 77

77 = 7 x 11

Step 2: Find the prime factorization of 82

82 = 2 x 41

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = = 1

Step 4: Therefore, the greatest common factor of 77 and 82 is 1