What is the Greatest Common Factor of 697 and 704?

Greatest common factor (GCF) of 697 and 704 is 1.

GCF(697,704) = 1

We will now calculate the prime factors of 697 and 704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 697 and 704.

How to find the GCF of 697 and 704?

We will first find the prime factorization of 697 and 704. After we will calculate the factors of 697 and 704 and find the biggest common factor number .

Step-1: Prime Factorization of 697

Prime factors of 697 are 17, 41. Prime factorization of 697 in exponential form is:

697 = 17¹ × 41¹

Step-2: Prime Factorization of 704

Prime factors of 704 are 2, 11. Prime factorization of 704 in exponential form is:

704 = 2⁶ × 11¹

Step-3: Factors of 697

List of positive integer factors of 697 that divides 697 without a remainder.

1, 17, 41

Step-4: Factors of 704

List of positive integer factors of 704 that divides 697 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 697 and 704. The biggest common factor number is the GCF number.
So the greatest common factor 697 and 704 is 1.

Also check out the Least Common Multiple of 697 and 704