What is the Greatest Common Factor of 73665 and 73680?

Greatest common factor (GCF) of 73665 and 73680 is 15.

GCF(73665,73680) = 15

We will now calculate the prime factors of 73665 and 73680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73665 and 73680.

How to find the GCF of 73665 and 73680?

We will first find the prime factorization of 73665 and 73680. After we will calculate the factors of 73665 and 73680 and find the biggest common factor number .

Step-1: Prime Factorization of 73665

Prime factors of 73665 are 3, 5, 1637. Prime factorization of 73665 in exponential form is:

73665 = 3² × 5¹ × 1637¹

Step-2: Prime Factorization of 73680

Prime factors of 73680 are 2, 3, 5, 307. Prime factorization of 73680 in exponential form is:

73680 = 2⁴ × 3¹ × 5¹ × 307¹

Step-3: Factors of 73665

List of positive integer factors of 73665 that divides 73665 without a remainder.

1, 3, 5, 9, 15, 45, 1637, 4911, 8185, 14733, 24555

Step-4: Factors of 73680

List of positive integer factors of 73680 that divides 73665 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 307, 614, 921, 1228, 1535, 1842, 2456, 3070, 3684, 4605, 4912, 6140, 7368, 9210, 12280, 14736, 18420, 24560, 36840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73665 and 73680. The biggest common factor number is the GCF number.
So the greatest common factor 73665 and 73680 is 15.

Also check out the Least Common Multiple of 73665 and 73680