What is the Greatest Common Factor of 65800 and 65814?

Greatest common factor (GCF) of 65800 and 65814 is 14.

GCF(65800,65814) = 14

We will now calculate the prime factors of 65800 and 65814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65800 and 65814.

How to find the GCF of 65800 and 65814?

We will first find the prime factorization of 65800 and 65814. After we will calculate the factors of 65800 and 65814 and find the biggest common factor number .

Step-1: Prime Factorization of 65800

Prime factors of 65800 are 2, 5, 7, 47. Prime factorization of 65800 in exponential form is:

65800 = 2³ × 5² × 7¹ × 47¹

Step-2: Prime Factorization of 65814

Prime factors of 65814 are 2, 3, 7, 1567. Prime factorization of 65814 in exponential form is:

65814 = 2¹ × 3¹ × 7¹ × 1567¹

Step-3: Factors of 65800

List of positive integer factors of 65800 that divides 65800 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 47, 50, 56, 70, 94, 100, 140, 175, 188, 200, 235, 280, 329, 350, 376, 470, 658, 700, 940, 1175, 1316, 1400, 1645, 1880, 2350, 2632, 3290, 4700, 6580, 8225, 9400, 13160, 16450, 32900

Step-4: Factors of 65814

List of positive integer factors of 65814 that divides 65800 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1567, 3134, 4701, 9402, 10969, 21938, 32907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65800 and 65814. The biggest common factor number is the GCF number.
So the greatest common factor 65800 and 65814 is 14.

Also check out the Least Common Multiple of 65800 and 65814