What is the Greatest Common Factor of 59760 and 59772?

Greatest common factor (GCF) of 59760 and 59772 is 12.

GCF(59760,59772) = 12

We will now calculate the prime factors of 59760 and 59772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59760 and 59772.

How to find the GCF of 59760 and 59772?

We will first find the prime factorization of 59760 and 59772. After we will calculate the factors of 59760 and 59772 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 59772

Prime factors of 59772 are 2, 3, 17, 293. Prime factorization of 59772 in exponential form is:

59772 = 2² × 3¹ × 17¹ × 293¹

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 59772

List of positive integer factors of 59772 that divides 59760 without a remainder.

1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204, 293, 586, 879, 1172, 1758, 3516, 4981, 9962, 14943, 19924, 29886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59760 and 59772. The biggest common factor number is the GCF number.
So the greatest common factor 59760 and 59772 is 12.

Also check out the Least Common Multiple of 59760 and 59772