What is the Greatest Common Factor of 60288 and 60300?

Greatest common factor (GCF) of 60288 and 60300 is 12.

GCF(60288,60300) = 12

We will now calculate the prime factors of 60288 and 60300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 60288 and 60300.

How to find the GCF of 60288 and 60300?

We will first find the prime factorization of 60288 and 60300. After we will calculate the factors of 60288 and 60300 and find the biggest common factor number .

Step-1: Prime Factorization of 60288

Prime factors of 60288 are 2, 3, 157. Prime factorization of 60288 in exponential form is:

60288 = 2⁷ × 3¹ × 157¹

Step-2: Prime Factorization of 60300

Prime factors of 60300 are 2, 3, 5, 67. Prime factorization of 60300 in exponential form is:

60300 = 2² × 3² × 5² × 67¹

Step-3: Factors of 60288

List of positive integer factors of 60288 that divides 60288 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 157, 192, 314, 384, 471, 628, 942, 1256, 1884, 2512, 3768, 5024, 7536, 10048, 15072, 20096, 30144

Step-4: Factors of 60300

List of positive integer factors of 60300 that divides 60288 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 67, 75, 90, 100, 134, 150, 180, 201, 225, 268, 300, 335, 402, 450, 603, 670, 804, 900, 1005, 1206, 1340, 1675, 2010, 2412, 3015, 3350, 4020, 5025, 6030, 6700, 10050, 12060, 15075, 20100, 30150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 60288 and 60300. The biggest common factor number is the GCF number.
So the greatest common factor 60288 and 60300 is 12.

Also check out the Least Common Multiple of 60288 and 60300