What is the Greatest Common Factor of 37698 and 37712?

Greatest common factor (GCF) of 37698 and 37712 is 2.

GCF(37698,37712) = 2

We will now calculate the prime factors of 37698 and 37712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37698 and 37712.

How to find the GCF of 37698 and 37712?

We will first find the prime factorization of 37698 and 37712. After we will calculate the factors of 37698 and 37712 and find the biggest common factor number .

Step-1: Prime Factorization of 37698

Prime factors of 37698 are 2, 3, 61, 103. Prime factorization of 37698 in exponential form is:

37698 = 2¹ × 3¹ × 61¹ × 103¹

Step-2: Prime Factorization of 37712

Prime factors of 37712 are 2, 2357. Prime factorization of 37712 in exponential form is:

37712 = 2⁴ × 2357¹

Step-3: Factors of 37698

List of positive integer factors of 37698 that divides 37698 without a remainder.

1, 2, 3, 6, 61, 103, 122, 183, 206, 309, 366, 618, 6283, 12566, 18849

Step-4: Factors of 37712

List of positive integer factors of 37712 that divides 37698 without a remainder.

1, 2, 4, 8, 16, 2357, 4714, 9428, 18856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37698 and 37712. The biggest common factor number is the GCF number.
So the greatest common factor 37698 and 37712 is 2.

Also check out the Least Common Multiple of 37698 and 37712