What is the Greatest Common Factor of 73149 and 73164?

Greatest common factor (GCF) of 73149 and 73164 is 3.

GCF(73149,73164) = 3

We will now calculate the prime factors of 73149 and 73164, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73149 and 73164.

How to find the GCF of 73149 and 73164?

We will first find the prime factorization of 73149 and 73164. After we will calculate the factors of 73149 and 73164 and find the biggest common factor number .

Step-1: Prime Factorization of 73149

Prime factors of 73149 are 3, 37, 659. Prime factorization of 73149 in exponential form is:

73149 = 3¹ × 37¹ × 659¹

Step-2: Prime Factorization of 73164

Prime factors of 73164 are 2, 3, 7, 13, 67. Prime factorization of 73164 in exponential form is:

73164 = 2² × 3¹ × 7¹ × 13¹ × 67¹

Step-3: Factors of 73149

List of positive integer factors of 73149 that divides 73149 without a remainder.

1, 3, 37, 111, 659, 1977, 24383

Step-4: Factors of 73164

List of positive integer factors of 73164 that divides 73149 without a remainder.

1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 67, 78, 84, 91, 134, 156, 182, 201, 268, 273, 364, 402, 469, 546, 804, 871, 938, 1092, 1407, 1742, 1876, 2613, 2814, 3484, 5226, 5628, 6097, 10452, 12194, 18291, 24388, 36582

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73149 and 73164. The biggest common factor number is the GCF number.
So the greatest common factor 73149 and 73164 is 3.

Also check out the Least Common Multiple of 73149 and 73164