What is the Greatest Common Factor of 715 and 735?

Greatest common factor (GCF) of 715 and 735 is 5.

GCF(715,735) = 5

We will now calculate the prime factors of 715 and 735, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 715 and 735.

How to find the GCF of 715 and 735?

We will first find the prime factorization of 715 and 735. After we will calculate the factors of 715 and 735 and find the biggest common factor number .

Step-1: Prime Factorization of 715

Prime factors of 715 are 5, 11, 13. Prime factorization of 715 in exponential form is:

715 = 5¹ × 11¹ × 13¹

Step-2: 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-3: Factors of 715

List of positive integer factors of 715 that divides 715 without a remainder.

1, 5, 11, 13, 55, 65, 143

Step-4: Factors of 735

List of positive integer factors of 735 that divides 715 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 715 and 735. The biggest common factor number is the GCF number.
So the greatest common factor 715 and 735 is 5.

Also check out the Least Common Multiple of 715 and 735