What is the Greatest Common Factor of 48084 and 48100?

Greatest common factor (GCF) of 48084 and 48100 is 4.

GCF(48084,48100) = 4

We will now calculate the prime factors of 48084 and 48100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48084 and 48100.

How to find the GCF of 48084 and 48100?

We will first find the prime factorization of 48084 and 48100. After we will calculate the factors of 48084 and 48100 and find the biggest common factor number .

Step-1: Prime Factorization of 48084

Prime factors of 48084 are 2, 3, 4007. Prime factorization of 48084 in exponential form is:

48084 = 2² × 3¹ × 4007¹

Step-2: Prime Factorization of 48100

Prime factors of 48100 are 2, 5, 13, 37. Prime factorization of 48100 in exponential form is:

48100 = 2² × 5² × 13¹ × 37¹

Step-3: Factors of 48084

List of positive integer factors of 48084 that divides 48084 without a remainder.

1, 2, 3, 4, 6, 12, 4007, 8014, 12021, 16028, 24042

Step-4: Factors of 48100

List of positive integer factors of 48100 that divides 48084 without a remainder.

1, 2, 4, 5, 10, 13, 20, 25, 26, 37, 50, 52, 65, 74, 100, 130, 148, 185, 260, 325, 370, 481, 650, 740, 925, 962, 1300, 1850, 1924, 2405, 3700, 4810, 9620, 12025, 24050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48084 and 48100. The biggest common factor number is the GCF number.
So the greatest common factor 48084 and 48100 is 4.

Also check out the Least Common Multiple of 48084 and 48100