What is the Greatest Common Factor of 749 and 763?

Greatest common factor (GCF) of 749 and 763 is 7.

GCF(749,763) = 7

We will now calculate the prime factors of 749 and 763, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 749 and 763.

How to find the GCF of 749 and 763?

We will first find the prime factorization of 749 and 763. After we will calculate the factors of 749 and 763 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 763

Prime factors of 763 are 7, 109. Prime factorization of 763 in exponential form is:

763 = 7¹ × 109¹

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 763

List of positive integer factors of 763 that divides 749 without a remainder.

1, 7, 109

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 749 and 763. The biggest common factor number is the GCF number.
So the greatest common factor 749 and 763 is 7.

Also check out the Least Common Multiple of 749 and 763