What is the Greatest Common Factor of 37145 and 37164?

Greatest common factor (GCF) of 37145 and 37164 is 19.

GCF(37145,37164) = 19

We will now calculate the prime factors of 37145 and 37164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37145 and 37164.

How to find the GCF of 37145 and 37164?

We will first find the prime factorization of 37145 and 37164. After we will calculate the factors of 37145 and 37164 and find the biggest common factor number .

Step-1: Prime Factorization of 37145

Prime factors of 37145 are 5, 17, 19, 23. Prime factorization of 37145 in exponential form is:

37145 = 5¹ × 17¹ × 19¹ × 23¹

Step-2: Prime Factorization of 37164

Prime factors of 37164 are 2, 3, 19, 163. Prime factorization of 37164 in exponential form is:

37164 = 2² × 3¹ × 19¹ × 163¹

Step-3: Factors of 37145

List of positive integer factors of 37145 that divides 37145 without a remainder.

1, 5, 17, 19, 23, 85, 95, 115, 323, 391, 437, 1615, 1955, 2185, 7429

Step-4: Factors of 37164

List of positive integer factors of 37164 that divides 37145 without a remainder.

1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 163, 228, 326, 489, 652, 978, 1956, 3097, 6194, 9291, 12388, 18582

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37145 and 37164. The biggest common factor number is the GCF number.
So the greatest common factor 37145 and 37164 is 19.

Also check out the Least Common Multiple of 37145 and 37164