What is the Greatest Common Factor of 689 and 708?

Greatest common factor (GCF) of 689 and 708 is 1.

GCF(689,708) = 1

We will now calculate the prime factors of 689 and 708, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 689 and 708.

How to find the GCF of 689 and 708?

We will first find the prime factorization of 689 and 708. After we will calculate the factors of 689 and 708 and find the biggest common factor number .

Step-1: Prime Factorization of 689

Prime factors of 689 are 13, 53. Prime factorization of 689 in exponential form is:

689 = 13¹ × 53¹

Step-2: Prime Factorization of 708

Prime factors of 708 are 2, 3, 59. Prime factorization of 708 in exponential form is:

708 = 2² × 3¹ × 59¹

Step-3: Factors of 689

List of positive integer factors of 689 that divides 689 without a remainder.

1, 13, 53

Step-4: Factors of 708

List of positive integer factors of 708 that divides 689 without a remainder.

1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 689 and 708. The biggest common factor number is the GCF number.
So the greatest common factor 689 and 708 is 1.

Also check out the Least Common Multiple of 689 and 708