What is the Greatest Common Factor of 38700 and 38714?

Greatest common factor (GCF) of 38700 and 38714 is 2.

GCF(38700,38714) = 2

We will now calculate the prime factors of 38700 and 38714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38700 and 38714.

How to find the GCF of 38700 and 38714?

We will first find the prime factorization of 38700 and 38714. After we will calculate the factors of 38700 and 38714 and find the biggest common factor number .

Step-1: Prime Factorization of 38700

Prime factors of 38700 are 2, 3, 5, 43. Prime factorization of 38700 in exponential form is:

38700 = 2² × 3² × 5² × 43¹

Step-2: Prime Factorization of 38714

Prime factors of 38714 are 2, 13, 1489. Prime factorization of 38714 in exponential form is:

38714 = 2¹ × 13¹ × 1489¹

Step-3: Factors of 38700

List of positive integer factors of 38700 that divides 38700 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 43, 45, 50, 60, 75, 86, 90, 100, 129, 150, 172, 180, 215, 225, 258, 300, 387, 430, 450, 516, 645, 774, 860, 900, 1075, 1290, 1548, 1935, 2150, 2580, 3225, 3870, 4300, 6450, 7740, 9675, 12900, 19350

Step-4: Factors of 38714

List of positive integer factors of 38714 that divides 38700 without a remainder.

1, 2, 13, 26, 1489, 2978, 19357

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38700 and 38714. The biggest common factor number is the GCF number.
So the greatest common factor 38700 and 38714 is 2.

Also check out the Least Common Multiple of 38700 and 38714