What is the Greatest Common Factor of 77214 and 77232?

Greatest common factor (GCF) of 77214 and 77232 is 6.

GCF(77214,77232) = 6

We will now calculate the prime factors of 77214 and 77232, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77214 and 77232.

How to find the GCF of 77214 and 77232?

We will first find the prime factorization of 77214 and 77232. After we will calculate the factors of 77214 and 77232 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 77232

Prime factors of 77232 are 2, 3, 1609. Prime factorization of 77232 in exponential form is:

77232 = 2⁴ × 3¹ × 1609¹

Step-3: Factors of 77214

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

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

Step-4: Factors of 77232

List of positive integer factors of 77232 that divides 77214 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1609, 3218, 4827, 6436, 9654, 12872, 19308, 25744, 38616

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77214 and 77232. The biggest common factor number is the GCF number.
So the greatest common factor 77214 and 77232 is 6.

Also check out the Least Common Multiple of 77214 and 77232