What is the Greatest Common Factor of 30084 and 30100?

Greatest common factor (GCF) of 30084 and 30100 is 4.

GCF(30084,30100) = 4

We will now calculate the prime factors of 30084 and 30100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30084 and 30100.

How to find the GCF of 30084 and 30100?

We will first find the prime factorization of 30084 and 30100. After we will calculate the factors of 30084 and 30100 and find the biggest common factor number .

Step-1: Prime Factorization of 30084

Prime factors of 30084 are 2, 3, 23, 109. Prime factorization of 30084 in exponential form is:

30084 = 2² × 3¹ × 23¹ × 109¹

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 30084

List of positive integer factors of 30084 that divides 30084 without a remainder.

1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 109, 138, 218, 276, 327, 436, 654, 1308, 2507, 5014, 7521, 10028, 15042

Step-4: Factors of 30100

List of positive integer factors of 30100 that divides 30084 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 30084 and 30100. The biggest common factor number is the GCF number.
So the greatest common factor 30084 and 30100 is 4.

Also check out the Least Common Multiple of 30084 and 30100