What is the Greatest Common Factor of 749 and 760?

Greatest common factor (GCF) of 749 and 760 is 1.

GCF(749,760) = 1

We will now calculate the prime factors of 749 and 760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 749 and 760.

How to find the GCF of 749 and 760?

We will first find the prime factorization of 749 and 760. After we will calculate the factors of 749 and 760 and find the biggest common factor number .

Step-1: Prime Factorization of 749

Prime factors of 749 are 7, 107. Prime factorization of 749 in exponential form is:

749 = 7¹ × 107¹

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 749

List of positive integer factors of 749 that divides 749 without a remainder.

1, 7, 107

Step-4: Factors of 760

List of positive integer factors of 760 that divides 749 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 749 and 760. The biggest common factor number is the GCF number.
So the greatest common factor 749 and 760 is 1.

Also check out the Least Common Multiple of 749 and 760