What is the Greatest Common Factor of 735 and 749?

Greatest common factor (GCF) of 735 and 749 is 7.

GCF(735,749) = 7

We will now calculate the prime factors of 735 and 749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 735 and 749.

How to find the GCF of 735 and 749?

We will first find the prime factorization of 735 and 749. After we will calculate the factors of 735 and 749 and find the biggest common factor number .

Step-1: Prime Factorization of 735

Prime factors of 735 are 3, 5, 7. Prime factorization of 735 in exponential form is:

735 = 3¹ × 5¹ × 7²

Step-2: Prime Factorization of 749

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

749 = 7¹ × 107¹

Step-3: Factors of 735

List of positive integer factors of 735 that divides 735 without a remainder.

1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245

Step-4: Factors of 749

List of positive integer factors of 749 that divides 735 without a remainder.

1, 7, 107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 735 and 749. The biggest common factor number is the GCF number.
So the greatest common factor 735 and 749 is 7.

Also check out the Least Common Multiple of 735 and 749