What is the Greatest Common Factor of 30086 and 30100?

Greatest common factor (GCF) of 30086 and 30100 is 14.

GCF(30086,30100) = 14

We will now calculate the prime factors of 30086 and 30100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30086 and 30100.

How to find the GCF of 30086 and 30100?

We will first find the prime factorization of 30086 and 30100. After we will calculate the factors of 30086 and 30100 and find the biggest common factor number .

Step-1: Prime Factorization of 30086

Prime factors of 30086 are 2, 7, 307. Prime factorization of 30086 in exponential form is:

30086 = 2¹ × 7² × 307¹

Step-2: Prime Factorization of 30100

Prime factors of 30100 are 2, 5, 7, 43. Prime factorization of 30100 in exponential form is:

30100 = 2² × 5² × 7¹ × 43¹

Step-3: Factors of 30086

List of positive integer factors of 30086 that divides 30086 without a remainder.

1, 2, 7, 14, 49, 98, 307, 614, 2149, 4298, 15043

Step-4: Factors of 30100

List of positive integer factors of 30100 that divides 30086 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 43, 50, 70, 86, 100, 140, 172, 175, 215, 301, 350, 430, 602, 700, 860, 1075, 1204, 1505, 2150, 3010, 4300, 6020, 7525, 15050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30086 and 30100. The biggest common factor number is the GCF number.
So the greatest common factor 30086 and 30100 is 14.

Also check out the Least Common Multiple of 30086 and 30100