What is the Greatest Common Factor of 76300 and 76314?

Greatest common factor (GCF) of 76300 and 76314 is 14.

GCF(76300,76314) = 14

We will now calculate the prime factors of 76300 and 76314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76300 and 76314.

How to find the GCF of 76300 and 76314?

We will first find the prime factorization of 76300 and 76314. After we will calculate the factors of 76300 and 76314 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 76314

Prime factors of 76314 are 2, 3, 7, 23, 79. Prime factorization of 76314 in exponential form is:

76314 = 2¹ × 3¹ × 7¹ × 23¹ × 79¹

Step-3: Factors of 76300

List of positive integer factors of 76300 that divides 76300 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

Step-4: Factors of 76314

List of positive integer factors of 76314 that divides 76300 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 79, 138, 158, 161, 237, 322, 474, 483, 553, 966, 1106, 1659, 1817, 3318, 3634, 5451, 10902, 12719, 25438, 38157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76300 and 76314. The biggest common factor number is the GCF number.
So the greatest common factor 76300 and 76314 is 14.

Also check out the Least Common Multiple of 76300 and 76314