What is the Greatest Common Factor of 37666 and 37672?

Greatest common factor (GCF) of 37666 and 37672 is 2.

GCF(37666,37672) = 2

We will now calculate the prime factors of 37666 and 37672, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37666 and 37672.

How to find the GCF of 37666 and 37672?

We will first find the prime factorization of 37666 and 37672. After we will calculate the factors of 37666 and 37672 and find the biggest common factor number .

Step-1: Prime Factorization of 37666

Prime factors of 37666 are 2, 37, 509. Prime factorization of 37666 in exponential form is:

37666 = 2¹ × 37¹ × 509¹

Step-2: Prime Factorization of 37672

Prime factors of 37672 are 2, 17, 277. Prime factorization of 37672 in exponential form is:

37672 = 2³ × 17¹ × 277¹

Step-3: Factors of 37666

List of positive integer factors of 37666 that divides 37666 without a remainder.

1, 2, 37, 74, 509, 1018, 18833

Step-4: Factors of 37672

List of positive integer factors of 37672 that divides 37666 without a remainder.

1, 2, 4, 8, 17, 34, 68, 136, 277, 554, 1108, 2216, 4709, 9418, 18836

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37666 and 37672. The biggest common factor number is the GCF number.
So the greatest common factor 37666 and 37672 is 2.

Also check out the Least Common Multiple of 37666 and 37672