What is the Greatest Common Factor of 29657 and 29664?

Greatest common factor (GCF) of 29657 and 29664 is 1.

GCF(29657,29664) = 1

We will now calculate the prime factors of 29657 and 29664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29657 and 29664.

How to find the GCF of 29657 and 29664?

We will first find the prime factorization of 29657 and 29664. After we will calculate the factors of 29657 and 29664 and find the biggest common factor number .

Step-1: Prime Factorization of 29657

Prime factors of 29657 are 47, 631. Prime factorization of 29657 in exponential form is:

29657 = 47¹ × 631¹

Step-2: Prime Factorization of 29664

Prime factors of 29664 are 2, 3, 103. Prime factorization of 29664 in exponential form is:

29664 = 2⁵ × 3² × 103¹

Step-3: Factors of 29657

List of positive integer factors of 29657 that divides 29657 without a remainder.

1, 47, 631

Step-4: Factors of 29664

List of positive integer factors of 29664 that divides 29657 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 103, 144, 206, 288, 309, 412, 618, 824, 927, 1236, 1648, 1854, 2472, 3296, 3708, 4944, 7416, 9888, 14832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29657 and 29664. The biggest common factor number is the GCF number.
So the greatest common factor 29657 and 29664 is 1.

Also check out the Least Common Multiple of 29657 and 29664