What is the Greatest Common Factor of 742 and 760?

Greatest common factor (GCF) of 742 and 760 is 2.

GCF(742,760) = 2

We will now calculate the prime factors of 742 and 760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 742 and 760.

How to find the GCF of 742 and 760?

We will first find the prime factorization of 742 and 760. After we will calculate the factors of 742 and 760 and find the biggest common factor number .

Step-1: Prime Factorization of 742

Prime factors of 742 are 2, 7, 53. Prime factorization of 742 in exponential form is:

742 = 2¹ × 7¹ × 53¹

Step-2: Prime Factorization of 760

Prime factors of 760 are 2, 5, 19. Prime factorization of 760 in exponential form is:

760 = 2³ × 5¹ × 19¹

Step-3: Factors of 742

List of positive integer factors of 742 that divides 742 without a remainder.

1, 2, 7, 14, 53, 106, 371

Step-4: Factors of 760

List of positive integer factors of 760 that divides 742 without a remainder.

1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 742 and 760. The biggest common factor number is the GCF number.
So the greatest common factor 742 and 760 is 2.

Also check out the Least Common Multiple of 742 and 760