What is the Greatest Common Factor of 37814 and 37828?

Greatest common factor (GCF) of 37814 and 37828 is 14.

GCF(37814,37828) = 14

We will now calculate the prime factors of 37814 and 37828, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37814 and 37828.

How to find the GCF of 37814 and 37828?

We will first find the prime factorization of 37814 and 37828. After we will calculate the factors of 37814 and 37828 and find the biggest common factor number .

Step-1: Prime Factorization of 37814

Prime factors of 37814 are 2, 7, 37, 73. Prime factorization of 37814 in exponential form is:

37814 = 2¹ × 7¹ × 37¹ × 73¹

Step-2: Prime Factorization of 37828

Prime factors of 37828 are 2, 7, 193. Prime factorization of 37828 in exponential form is:

37828 = 2² × 7² × 193¹

Step-3: Factors of 37814

List of positive integer factors of 37814 that divides 37814 without a remainder.

1, 2, 7, 14, 37, 73, 74, 146, 259, 511, 518, 1022, 2701, 5402, 18907

Step-4: Factors of 37828

List of positive integer factors of 37828 that divides 37814 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 193, 196, 386, 772, 1351, 2702, 5404, 9457, 18914

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37814 and 37828. The biggest common factor number is the GCF number.
So the greatest common factor 37814 and 37828 is 14.

Also check out the Least Common Multiple of 37814 and 37828