What is the Greatest Common Factor of 72704 and 72720?

Greatest common factor (GCF) of 72704 and 72720 is 16.

GCF(72704,72720) = 16

We will now calculate the prime factors of 72704 and 72720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72704 and 72720.

How to find the GCF of 72704 and 72720?

We will first find the prime factorization of 72704 and 72720. After we will calculate the factors of 72704 and 72720 and find the biggest common factor number .

Step-1: Prime Factorization of 72704

Prime factors of 72704 are 2, 71. Prime factorization of 72704 in exponential form is:

72704 = 2¹⁰ × 71¹

Step-2: Prime Factorization of 72720

Prime factors of 72720 are 2, 3, 5, 101. Prime factorization of 72720 in exponential form is:

72720 = 2⁴ × 3² × 5¹ × 101¹

Step-3: Factors of 72704

List of positive integer factors of 72704 that divides 72704 without a remainder.

1, 2, 4, 8, 16, 32, 64, 71, 128, 142, 256, 284, 512, 568, 1024, 1136, 2272, 4544, 9088, 18176, 36352

Step-4: Factors of 72720

List of positive integer factors of 72720 that divides 72704 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 101, 120, 144, 180, 202, 240, 303, 360, 404, 505, 606, 720, 808, 909, 1010, 1212, 1515, 1616, 1818, 2020, 2424, 3030, 3636, 4040, 4545, 4848, 6060, 7272, 8080, 9090, 12120, 14544, 18180, 24240, 36360

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72704 and 72720. The biggest common factor number is the GCF number.
So the greatest common factor 72704 and 72720 is 16.

Also check out the Least Common Multiple of 72704 and 72720