What is the Greatest Common Factor of 39689 and 39702?

Greatest common factor (GCF) of 39689 and 39702 is 13.

GCF(39689,39702) = 13

We will now calculate the prime factors of 39689 and 39702, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39689 and 39702.

How to find the GCF of 39689 and 39702?

We will first find the prime factorization of 39689 and 39702. After we will calculate the factors of 39689 and 39702 and find the biggest common factor number .

Step-1: Prime Factorization of 39689

Prime factors of 39689 are 13, 43, 71. Prime factorization of 39689 in exponential form is:

39689 = 13¹ × 43¹ × 71¹

Step-2: Prime Factorization of 39702

Prime factors of 39702 are 2, 3, 13, 509. Prime factorization of 39702 in exponential form is:

39702 = 2¹ × 3¹ × 13¹ × 509¹

Step-3: Factors of 39689

List of positive integer factors of 39689 that divides 39689 without a remainder.

1, 13, 43, 71, 559, 923, 3053

Step-4: Factors of 39702

List of positive integer factors of 39702 that divides 39689 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 509, 1018, 1527, 3054, 6617, 13234, 19851

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39689 and 39702. The biggest common factor number is the GCF number.
So the greatest common factor 39689 and 39702 is 13.

Also check out the Least Common Multiple of 39689 and 39702