What is the Greatest Common Factor of 27914 and 27930?

Greatest common factor (GCF) of 27914 and 27930 is 2.

GCF(27914,27930) = 2

We will now calculate the prime factors of 27914 and 27930, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27914 and 27930.

How to find the GCF of 27914 and 27930?

We will first find the prime factorization of 27914 and 27930. After we will calculate the factors of 27914 and 27930 and find the biggest common factor number .

Step-1: Prime Factorization of 27914

Prime factors of 27914 are 2, 17, 821. Prime factorization of 27914 in exponential form is:

27914 = 2¹ × 17¹ × 821¹

Step-2: Prime Factorization of 27930

Prime factors of 27930 are 2, 3, 5, 7, 19. Prime factorization of 27930 in exponential form is:

27930 = 2¹ × 3¹ × 5¹ × 7² × 19¹

Step-3: Factors of 27914

List of positive integer factors of 27914 that divides 27914 without a remainder.

1, 2, 17, 34, 821, 1642, 13957

Step-4: Factors of 27930

List of positive integer factors of 27930 that divides 27914 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 19, 21, 30, 35, 38, 42, 49, 57, 70, 95, 98, 105, 114, 133, 147, 190, 210, 245, 266, 285, 294, 399, 490, 570, 665, 735, 798, 931, 1330, 1470, 1862, 1995, 2793, 3990, 4655, 5586, 9310, 13965

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27914 and 27930. The biggest common factor number is the GCF number.
So the greatest common factor 27914 and 27930 is 2.

Also check out the Least Common Multiple of 27914 and 27930