What is the Greatest Common Factor of 14700 and 14714?

Greatest common factor (GCF) of 14700 and 14714 is 14.

GCF(14700,14714) = 14

We will now calculate the prime factors of 14700 and 14714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14700 and 14714.

How to find the GCF of 14700 and 14714?

We will first find the prime factorization of 14700 and 14714. After we will calculate the factors of 14700 and 14714 and find the biggest common factor number .

Step-1: Prime Factorization of 14700

Prime factors of 14700 are 2, 3, 5, 7. Prime factorization of 14700 in exponential form is:

14700 = 2² × 3¹ × 5² × 7²

Step-2: Prime Factorization of 14714

Prime factors of 14714 are 2, 7, 1051. Prime factorization of 14714 in exponential form is:

14714 = 2¹ × 7¹ × 1051¹

Step-3: Factors of 14700

List of positive integer factors of 14700 that divides 14700 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 49, 50, 60, 70, 75, 84, 98, 100, 105, 140, 147, 150, 175, 196, 210, 245, 294, 300, 350, 420, 490, 525, 588, 700, 735, 980, 1050, 1225, 1470, 2100, 2450, 2940, 3675, 4900, 7350

Step-4: Factors of 14714

List of positive integer factors of 14714 that divides 14700 without a remainder.

1, 2, 7, 14, 1051, 2102, 7357

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14700 and 14714. The biggest common factor number is the GCF number.
So the greatest common factor 14700 and 14714 is 14.

Also check out the Least Common Multiple of 14700 and 14714