What is the Greatest Common Factor of 76500 and 76512?

Greatest common factor (GCF) of 76500 and 76512 is 12.

GCF(76500,76512) = 12

We will now calculate the prime factors of 76500 and 76512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76500 and 76512.

How to find the GCF of 76500 and 76512?

We will first find the prime factorization of 76500 and 76512. After we will calculate the factors of 76500 and 76512 and find the biggest common factor number .

Step-1: Prime Factorization of 76500

Prime factors of 76500 are 2, 3, 5, 17. Prime factorization of 76500 in exponential form is:

76500 = 2² × 3² × 5³ × 17¹

Step-2: Prime Factorization of 76512

Prime factors of 76512 are 2, 3, 797. Prime factorization of 76512 in exponential form is:

76512 = 2⁵ × 3¹ × 797¹

Step-3: Factors of 76500

List of positive integer factors of 76500 that divides 76500 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 25, 30, 34, 36, 45, 50, 51, 60, 68, 75, 85, 90, 100, 102, 125, 150, 153, 170, 180, 204, 225, 250, 255, 300, 306, 340, 375, 425, 450, 500, 510, 612, 750, 765, 850, 900, 1020, 1125, 1275, 1500, 1530, 1700, 2125, 2250, 2550, 3060, 3825, 4250, 4500, 5100, 6375, 7650, 8500, 12750, 15300, 19125, 25500, 38250

Step-4: Factors of 76512

List of positive integer factors of 76512 that divides 76500 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 797, 1594, 2391, 3188, 4782, 6376, 9564, 12752, 19128, 25504, 38256

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76500 and 76512. The biggest common factor number is the GCF number.
So the greatest common factor 76500 and 76512 is 12.

Also check out the Least Common Multiple of 76500 and 76512