What is the Greatest Common Factor of 76480 and 76500?

Greatest common factor (GCF) of 76480 and 76500 is 20.

GCF(76480,76500) = 20

We will now calculate the prime factors of 76480 and 76500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76480 and 76500.

How to find the GCF of 76480 and 76500?

We will first find the prime factorization of 76480 and 76500. After we will calculate the factors of 76480 and 76500 and find the biggest common factor number .

Step-1: Prime Factorization of 76480

Prime factors of 76480 are 2, 5, 239. Prime factorization of 76480 in exponential form is:

76480 = 2⁶ × 5¹ × 239¹

Step-2: 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-3: Factors of 76480

List of positive integer factors of 76480 that divides 76480 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 239, 320, 478, 956, 1195, 1912, 2390, 3824, 4780, 7648, 9560, 15296, 19120, 38240

Step-4: Factors of 76500

List of positive integer factors of 76500 that divides 76480 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76480 and 76500. The biggest common factor number is the GCF number.
So the greatest common factor 76480 and 76500 is 20.

Also check out the Least Common Multiple of 76480 and 76500