What is the Greatest Common Factor of 64500 and 64512?

Greatest common factor (GCF) of 64500 and 64512 is 12.

GCF(64500,64512) = 12

We will now calculate the prime factors of 64500 and 64512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 64500 and 64512.

How to find the GCF of 64500 and 64512?

We will first find the prime factorization of 64500 and 64512. After we will calculate the factors of 64500 and 64512 and find the biggest common factor number .

Step-1: Prime Factorization of 64500

Prime factors of 64500 are 2, 3, 5, 43. Prime factorization of 64500 in exponential form is:

64500 = 2² × 3¹ × 5³ × 43¹

Step-2: Prime Factorization of 64512

Prime factors of 64512 are 2, 3, 7. Prime factorization of 64512 in exponential form is:

64512 = 2¹⁰ × 3² × 7¹

Step-3: Factors of 64500

List of positive integer factors of 64500 that divides 64500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 43, 50, 60, 75, 86, 100, 125, 129, 150, 172, 215, 250, 258, 300, 375, 430, 500, 516, 645, 750, 860, 1075, 1290, 1500, 2150, 2580, 3225, 4300, 5375, 6450, 10750, 12900, 16125, 21500, 32250

Step-4: Factors of 64512

List of positive integer factors of 64512 that divides 64500 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 256, 288, 336, 384, 448, 504, 512, 576, 672, 768, 896, 1008, 1024, 1152, 1344, 1536, 1792, 2016, 2304, 2688, 3072, 3584, 4032, 4608, 5376, 7168, 8064, 9216, 10752, 16128, 21504, 32256

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 64500 and 64512. The biggest common factor number is the GCF number.
So the greatest common factor 64500 and 64512 is 12.

Also check out the Least Common Multiple of 64500 and 64512