What is the Greatest Common Factor of 72314 and 72320?

Greatest common factor (GCF) of 72314 and 72320 is 2.

GCF(72314,72320) = 2

We will now calculate the prime factors of 72314 and 72320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72314 and 72320.

How to find the GCF of 72314 and 72320?

We will first find the prime factorization of 72314 and 72320. After we will calculate the factors of 72314 and 72320 and find the biggest common factor number .

Step-1: Prime Factorization of 72314

Prime factors of 72314 are 2, 11, 19, 173. Prime factorization of 72314 in exponential form is:

72314 = 2¹ × 11¹ × 19¹ × 173¹

Step-2: Prime Factorization of 72320

Prime factors of 72320 are 2, 5, 113. Prime factorization of 72320 in exponential form is:

72320 = 2⁷ × 5¹ × 113¹

Step-3: Factors of 72314

List of positive integer factors of 72314 that divides 72314 without a remainder.

1, 2, 11, 19, 22, 38, 173, 209, 346, 418, 1903, 3287, 3806, 6574, 36157

Step-4: Factors of 72320

List of positive integer factors of 72320 that divides 72314 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 113, 128, 160, 226, 320, 452, 565, 640, 904, 1130, 1808, 2260, 3616, 4520, 7232, 9040, 14464, 18080, 36160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72314 and 72320. The biggest common factor number is the GCF number.
So the greatest common factor 72314 and 72320 is 2.

Also check out the Least Common Multiple of 72314 and 72320