What is the Greatest Common Factor of 76208 and 76214?

Greatest common factor (GCF) of 76208 and 76214 is 2.

GCF(76208,76214) = 2

We will now calculate the prime factors of 76208 and 76214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76208 and 76214.

How to find the GCF of 76208 and 76214?

We will first find the prime factorization of 76208 and 76214. After we will calculate the factors of 76208 and 76214 and find the biggest common factor number .

Step-1: Prime Factorization of 76208

Prime factors of 76208 are 2, 11, 433. Prime factorization of 76208 in exponential form is:

76208 = 2⁴ × 11¹ × 433¹

Step-2: Prime Factorization of 76214

Prime factors of 76214 are 2, 53, 719. Prime factorization of 76214 in exponential form is:

76214 = 2¹ × 53¹ × 719¹

Step-3: Factors of 76208

List of positive integer factors of 76208 that divides 76208 without a remainder.

1, 2, 4, 8, 11, 16, 22, 44, 88, 176, 433, 866, 1732, 3464, 4763, 6928, 9526, 19052, 38104

Step-4: Factors of 76214

List of positive integer factors of 76214 that divides 76208 without a remainder.

1, 2, 53, 106, 719, 1438, 38107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76208 and 76214. The biggest common factor number is the GCF number.
So the greatest common factor 76208 and 76214 is 2.

Also check out the Least Common Multiple of 76208 and 76214