What is the Greatest Common Factor of 37809 and 37814?

Greatest common factor (GCF) of 37809 and 37814 is 1.

GCF(37809,37814) = 1

We will now calculate the prime factors of 37809 and 37814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37809 and 37814.

How to find the GCF of 37809 and 37814?

We will first find the prime factorization of 37809 and 37814. After we will calculate the factors of 37809 and 37814 and find the biggest common factor number .

Step-1: Prime Factorization of 37809

Prime factors of 37809 are 3, 4201. Prime factorization of 37809 in exponential form is:

37809 = 3² × 4201¹

Step-2: 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-3: Factors of 37809

List of positive integer factors of 37809 that divides 37809 without a remainder.

1, 3, 9, 4201, 12603

Step-4: Factors of 37814

List of positive integer factors of 37814 that divides 37809 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37809 and 37814. The biggest common factor number is the GCF number.
So the greatest common factor 37809 and 37814 is 1.

Also check out the Least Common Multiple of 37809 and 37814