What is the Greatest Common Factor of 738 and 753?

Greatest common factor (GCF) of 738 and 753 is 3.

GCF(738,753) = 3

We will now calculate the prime factors of 738 and 753, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 738 and 753.

How to find the GCF of 738 and 753?

We will first find the prime factorization of 738 and 753. After we will calculate the factors of 738 and 753 and find the biggest common factor number .

Step-1: Prime Factorization of 738

Prime factors of 738 are 2, 3, 41. Prime factorization of 738 in exponential form is:

738 = 2¹ × 3² × 41¹

Step-2: Prime Factorization of 753

Prime factors of 753 are 3, 251. Prime factorization of 753 in exponential form is:

753 = 3¹ × 251¹

Step-3: Factors of 738

List of positive integer factors of 738 that divides 738 without a remainder.

1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369

Step-4: Factors of 753

List of positive integer factors of 753 that divides 738 without a remainder.

1, 3, 251

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 738 and 753. The biggest common factor number is the GCF number.
So the greatest common factor 738 and 753 is 3.

Also check out the Least Common Multiple of 738 and 753