What is the Greatest Common Factor of 76500 and 76514?

Greatest common factor (GCF) of 76500 and 76514 is 2.

GCF(76500,76514) = 2

We will now calculate the prime factors of 76500 and 76514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76500 and 76514.

How to find the GCF of 76500 and 76514?

We will first find the prime factorization of 76500 and 76514. After we will calculate the factors of 76500 and 76514 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 76514

Prime factors of 76514 are 2, 67, 571. Prime factorization of 76514 in exponential form is:

76514 = 2¹ × 67¹ × 571¹

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 76514

List of positive integer factors of 76514 that divides 76500 without a remainder.

1, 2, 67, 134, 571, 1142, 38257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76500 and 76514. The biggest common factor number is the GCF number.
So the greatest common factor 76500 and 76514 is 2.

Also check out the Least Common Multiple of 76500 and 76514