What is the Greatest Common Factor of 37814 and 37822?

Greatest common factor (GCF) of 37814 and 37822 is 2.

GCF(37814,37822) = 2

We will now calculate the prime factors of 37814 and 37822, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37814 and 37822.

How to find the GCF of 37814 and 37822?

We will first find the prime factorization of 37814 and 37822. After we will calculate the factors of 37814 and 37822 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 37822

Prime factors of 37822 are 2, 18911. Prime factorization of 37822 in exponential form is:

37822 = 2¹ × 18911¹

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 37822

List of positive integer factors of 37822 that divides 37814 without a remainder.

1, 2, 18911

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37814 and 37822. The biggest common factor number is the GCF number.
So the greatest common factor 37814 and 37822 is 2.

Also check out the Least Common Multiple of 37814 and 37822