What is the Greatest Common Factor of 30740 and 30758?

Greatest common factor (GCF) of 30740 and 30758 is 2.

GCF(30740,30758) = 2

We will now calculate the prime factors of 30740 and 30758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30740 and 30758.

How to find the GCF of 30740 and 30758?

We will first find the prime factorization of 30740 and 30758. After we will calculate the factors of 30740 and 30758 and find the biggest common factor number .

Step-1: Prime Factorization of 30740

Prime factors of 30740 are 2, 5, 29, 53. Prime factorization of 30740 in exponential form is:

30740 = 2² × 5¹ × 29¹ × 53¹

Step-2: 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-3: Factors of 30740

List of positive integer factors of 30740 that divides 30740 without a remainder.

1, 2, 4, 5, 10, 20, 29, 53, 58, 106, 116, 145, 212, 265, 290, 530, 580, 1060, 1537, 3074, 6148, 7685, 15370

Step-4: Factors of 30758

List of positive integer factors of 30758 that divides 30740 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30740 and 30758. The biggest common factor number is the GCF number.
So the greatest common factor 30740 and 30758 is 2.

Also check out the Least Common Multiple of 30740 and 30758