What is the Greatest Common Factor of 71750 and 71764?

Greatest common factor (GCF) of 71750 and 71764 is 14.

GCF(71750,71764) = 14

We will now calculate the prime factors of 71750 and 71764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71750 and 71764.

How to find the GCF of 71750 and 71764?

We will first find the prime factorization of 71750 and 71764. After we will calculate the factors of 71750 and 71764 and find the biggest common factor number .

Step-1: Prime Factorization of 71750

Prime factors of 71750 are 2, 5, 7, 41. Prime factorization of 71750 in exponential form is:

71750 = 2¹ × 5³ × 7¹ × 41¹

Step-2: Prime Factorization of 71764

Prime factors of 71764 are 2, 7, 11, 233. Prime factorization of 71764 in exponential form is:

71764 = 2² × 7¹ × 11¹ × 233¹

Step-3: Factors of 71750

List of positive integer factors of 71750 that divides 71750 without a remainder.

1, 2, 5, 7, 10, 14, 25, 35, 41, 50, 70, 82, 125, 175, 205, 250, 287, 350, 410, 574, 875, 1025, 1435, 1750, 2050, 2870, 5125, 7175, 10250, 14350, 35875

Step-4: Factors of 71764

List of positive integer factors of 71764 that divides 71750 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 233, 308, 466, 932, 1631, 2563, 3262, 5126, 6524, 10252, 17941, 35882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71750 and 71764. The biggest common factor number is the GCF number.
So the greatest common factor 71750 and 71764 is 14.

Also check out the Least Common Multiple of 71750 and 71764