What is the Greatest Common Factor of 76286 and 76300?

Greatest common factor (GCF) of 76286 and 76300 is 14.

GCF(76286,76300) = 14

We will now calculate the prime factors of 76286 and 76300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76286 and 76300.

How to find the GCF of 76286 and 76300?

We will first find the prime factorization of 76286 and 76300. After we will calculate the factors of 76286 and 76300 and find the biggest common factor number .

Step-1: Prime Factorization of 76286

Prime factors of 76286 are 2, 7, 5449. Prime factorization of 76286 in exponential form is:

76286 = 2¹ × 7¹ × 5449¹

Step-2: Prime Factorization of 76300

Prime factors of 76300 are 2, 5, 7, 109. Prime factorization of 76300 in exponential form is:

76300 = 2² × 5² × 7¹ × 109¹

Step-3: Factors of 76286

List of positive integer factors of 76286 that divides 76286 without a remainder.

1, 2, 7, 14, 5449, 10898, 38143

Step-4: Factors of 76300

List of positive integer factors of 76300 that divides 76286 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 109, 140, 175, 218, 350, 436, 545, 700, 763, 1090, 1526, 2180, 2725, 3052, 3815, 5450, 7630, 10900, 15260, 19075, 38150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76286 and 76300. The biggest common factor number is the GCF number.
So the greatest common factor 76286 and 76300 is 14.

Also check out the Least Common Multiple of 76286 and 76300