What is the Greatest Common Factor of 59760 and 59775?

Greatest common factor (GCF) of 59760 and 59775 is 15.

GCF(59760,59775) = 15

We will now calculate the prime factors of 59760 and 59775, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59760 and 59775.

How to find the GCF of 59760 and 59775?

We will first find the prime factorization of 59760 and 59775. After we will calculate the factors of 59760 and 59775 and find the biggest common factor number .

Step-1: Prime Factorization of 59760

Prime factors of 59760 are 2, 3, 5, 83. Prime factorization of 59760 in exponential form is:

59760 = 2⁴ × 3² × 5¹ × 83¹

Step-2: Prime Factorization of 59775

Prime factors of 59775 are 3, 5, 797. Prime factorization of 59775 in exponential form is:

59775 = 3¹ × 5² × 797¹

Step-3: Factors of 59760

List of positive integer factors of 59760 that divides 59760 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, 83, 90, 120, 144, 166, 180, 240, 249, 332, 360, 415, 498, 664, 720, 747, 830, 996, 1245, 1328, 1494, 1660, 1992, 2490, 2988, 3320, 3735, 3984, 4980, 5976, 6640, 7470, 9960, 11952, 14940, 19920, 29880

Step-4: Factors of 59775

List of positive integer factors of 59775 that divides 59760 without a remainder.

1, 3, 5, 15, 25, 75, 797, 2391, 3985, 11955, 19925

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59760 and 59775. The biggest common factor number is the GCF number.
So the greatest common factor 59760 and 59775 is 15.

Also check out the Least Common Multiple of 59760 and 59775