What is the Greatest Common Factor of 36 and 51?

Greatest common factor (GCF) of 36 and 51 is 3.

GCF(36,51) = 3

We will now calculate the prime factors of 36 and 51, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36 and 51.

How to find the GCF of 36 and 51?

We will first find the prime factorization of 36 and 51. After we will calculate the factors of 36 and 51 and find the biggest common factor number .

Step-1: Prime Factorization of 36

Prime factors of 36 are 2, 3. Prime factorization of 36 in exponential form is:

36 = 2² × 3²

Step-2: Prime Factorization of 51

Prime factors of 51 are 3, 17. Prime factorization of 51 in exponential form is:

51 = 3¹ × 17¹

Step-3: Factors of 36

List of positive integer factors of 36 that divides 36 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18

Step-4: Factors of 51

List of positive integer factors of 51 that divides 36 without a remainder.

1, 3, 17

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36 and 51. The biggest common factor number is the GCF number.
So the greatest common factor 36 and 51 is 3.

Also check out the Least Common Multiple of 36 and 51