What is the Greatest Common Factor of 29646 and 29664?

Greatest common factor (GCF) of 29646 and 29664 is 18.

GCF(29646,29664) = 18

We will now calculate the prime factors of 29646 and 29664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29646 and 29664.

How to find the GCF of 29646 and 29664?

We will first find the prime factorization of 29646 and 29664. After we will calculate the factors of 29646 and 29664 and find the biggest common factor number .

Step-1: Prime Factorization of 29646

Prime factors of 29646 are 2, 3, 61. Prime factorization of 29646 in exponential form is:

29646 = 2¹ × 3⁵ × 61¹

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 29646

List of positive integer factors of 29646 that divides 29646 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 61, 81, 122, 162, 183, 243, 366, 486, 549, 1098, 1647, 3294, 4941, 9882, 14823

Step-4: Factors of 29664

List of positive integer factors of 29664 that divides 29646 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 29646 and 29664. The biggest common factor number is the GCF number.
So the greatest common factor 29646 and 29664 is 18.

Also check out the Least Common Multiple of 29646 and 29664