What is the Greatest Common Factor of 72086 and 72100?

Greatest common factor (GCF) of 72086 and 72100 is 14.

GCF(72086,72100) = 14

We will now calculate the prime factors of 72086 and 72100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 72086 and 72100.

How to find the GCF of 72086 and 72100?

We will first find the prime factorization of 72086 and 72100. After we will calculate the factors of 72086 and 72100 and find the biggest common factor number .

Step-1: Prime Factorization of 72086

Prime factors of 72086 are 2, 7, 19, 271. Prime factorization of 72086 in exponential form is:

72086 = 2¹ × 7¹ × 19¹ × 271¹

Step-2: Prime Factorization of 72100

Prime factors of 72100 are 2, 5, 7, 103. Prime factorization of 72100 in exponential form is:

72100 = 2² × 5² × 7¹ × 103¹

Step-3: Factors of 72086

List of positive integer factors of 72086 that divides 72086 without a remainder.

1, 2, 7, 14, 19, 38, 133, 266, 271, 542, 1897, 3794, 5149, 10298, 36043

Step-4: Factors of 72100

List of positive integer factors of 72100 that divides 72086 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 103, 140, 175, 206, 350, 412, 515, 700, 721, 1030, 1442, 2060, 2575, 2884, 3605, 5150, 7210, 10300, 14420, 18025, 36050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 72086 and 72100. The biggest common factor number is the GCF number.
So the greatest common factor 72086 and 72100 is 14.

Also check out the Least Common Multiple of 72086 and 72100