What is the Greatest Common Factor of 30758 and 30774?

Greatest common factor (GCF) of 30758 and 30774 is 2.

GCF(30758,30774) = 2

We will now calculate the prime factors of 30758 and 30774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30758 and 30774.

How to find the GCF of 30758 and 30774?

We will first find the prime factorization of 30758 and 30774. After we will calculate the factors of 30758 and 30774 and find the biggest common factor number .

Step-1: Prime Factorization of 30758

Prime factors of 30758 are 2, 7, 13. Prime factorization of 30758 in exponential form is:

30758 = 2¹ × 7¹ × 13³

Step-2: Prime Factorization of 30774

Prime factors of 30774 are 2, 3, 23, 223. Prime factorization of 30774 in exponential form is:

30774 = 2¹ × 3¹ × 23¹ × 223¹

Step-3: Factors of 30758

List of positive integer factors of 30758 that divides 30758 without a remainder.

1, 2, 7, 13, 14, 26, 91, 169, 182, 338, 1183, 2197, 2366, 4394, 15379

Step-4: Factors of 30774

List of positive integer factors of 30774 that divides 30758 without a remainder.

1, 2, 3, 6, 23, 46, 69, 138, 223, 446, 669, 1338, 5129, 10258, 15387

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30758 and 30774. The biggest common factor number is the GCF number.
So the greatest common factor 30758 and 30774 is 2.

Also check out the Least Common Multiple of 30758 and 30774