What is the Greatest Common Factor of 14700 and 14705?

Greatest common factor (GCF) of 14700 and 14705 is 5.

GCF(14700,14705) = 5

We will now calculate the prime factors of 14700 and 14705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14700 and 14705.

How to find the GCF of 14700 and 14705?

We will first find the prime factorization of 14700 and 14705. After we will calculate the factors of 14700 and 14705 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 14705

Prime factors of 14705 are 5, 17, 173. Prime factorization of 14705 in exponential form is:

14705 = 5¹ × 17¹ × 173¹

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 14705

List of positive integer factors of 14705 that divides 14700 without a remainder.

1, 5, 17, 85, 173, 865, 2941

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14700 and 14705. The biggest common factor number is the GCF number.
So the greatest common factor 14700 and 14705 is 5.

Also check out the Least Common Multiple of 14700 and 14705