What is the Greatest Common Factor of 30114 and 30121?

Greatest common factor (GCF) of 30114 and 30121 is 7.

GCF(30114,30121) = 7

We will now calculate the prime factors of 30114 and 30121, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30114 and 30121.

How to find the GCF of 30114 and 30121?

We will first find the prime factorization of 30114 and 30121. After we will calculate the factors of 30114 and 30121 and find the biggest common factor number .

Step-1: Prime Factorization of 30114

Prime factors of 30114 are 2, 3, 7, 239. Prime factorization of 30114 in exponential form is:

30114 = 2¹ × 3² × 7¹ × 239¹

Step-2: Prime Factorization of 30121

Prime factors of 30121 are 7, 13, 331. Prime factorization of 30121 in exponential form is:

30121 = 7¹ × 13¹ × 331¹

Step-3: Factors of 30114

List of positive integer factors of 30114 that divides 30114 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 239, 478, 717, 1434, 1673, 2151, 3346, 4302, 5019, 10038, 15057

Step-4: Factors of 30121

List of positive integer factors of 30121 that divides 30114 without a remainder.

1, 7, 13, 91, 331, 2317, 4303

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30114 and 30121. The biggest common factor number is the GCF number.
So the greatest common factor 30114 and 30121 is 7.

Also check out the Least Common Multiple of 30114 and 30121