What is the Greatest Common Factor of 38 and 45?

Greatest common factor (GCF) of 38 and 45 is 1.

GCF(38,45) = 1

We will now calculate the prime factors of 38 and 45, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38 and 45.

How to find the GCF of 38 and 45?

We will first find the prime factorization of 38 and 45. After we will calculate the factors of 38 and 45 and find the biggest common factor number .

Step-1: Prime Factorization of 38

Prime factors of 38 are 2, 19. Prime factorization of 38 in exponential form is:

38 = 2¹ × 19¹

Step-2: Prime Factorization of 45

Prime factors of 45 are 3, 5. Prime factorization of 45 in exponential form is:

45 = 3² × 5¹

Step-3: Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1, 2, 19

Step-4: Factors of 45

List of positive integer factors of 45 that divides 38 without a remainder.

1, 3, 5, 9, 15

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38 and 45. The biggest common factor number is the GCF number.
So the greatest common factor 38 and 45 is 1.

Also check out the Least Common Multiple of 38 and 45