What is the Greatest Common Factor of 77205 and 77214?

Greatest common factor (GCF) of 77205 and 77214 is 3.

GCF(77205,77214) = 3

We will now calculate the prime factors of 77205 and 77214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77205 and 77214.

How to find the GCF of 77205 and 77214?

We will first find the prime factorization of 77205 and 77214. After we will calculate the factors of 77205 and 77214 and find the biggest common factor number .

Step-1: Prime Factorization of 77205

Prime factors of 77205 are 3, 5, 5147. Prime factorization of 77205 in exponential form is:

77205 = 3¹ × 5¹ × 5147¹

Step-2: Prime Factorization of 77214

Prime factors of 77214 are 2, 3, 17, 757. Prime factorization of 77214 in exponential form is:

77214 = 2¹ × 3¹ × 17¹ × 757¹

Step-3: Factors of 77205

List of positive integer factors of 77205 that divides 77205 without a remainder.

1, 3, 5, 15, 5147, 15441, 25735

Step-4: Factors of 77214

List of positive integer factors of 77214 that divides 77205 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 757, 1514, 2271, 4542, 12869, 25738, 38607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77205 and 77214. The biggest common factor number is the GCF number.
So the greatest common factor 77205 and 77214 is 3.

Also check out the Least Common Multiple of 77205 and 77214