What is the Greatest Common Factor of 48090 and 48100?

Greatest common factor (GCF) of 48090 and 48100 is 10.

GCF(48090,48100) = 10

We will now calculate the prime factors of 48090 and 48100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48090 and 48100.

How to find the GCF of 48090 and 48100?

We will first find the prime factorization of 48090 and 48100. After we will calculate the factors of 48090 and 48100 and find the biggest common factor number .

Step-1: Prime Factorization of 48090

Prime factors of 48090 are 2, 3, 5, 7, 229. Prime factorization of 48090 in exponential form is:

48090 = 2¹ × 3¹ × 5¹ × 7¹ × 229¹

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 48090

List of positive integer factors of 48090 that divides 48090 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210, 229, 458, 687, 1145, 1374, 1603, 2290, 3206, 3435, 4809, 6870, 8015, 9618, 16030, 24045

Step-4: Factors of 48100

List of positive integer factors of 48100 that divides 48090 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 48090 and 48100. The biggest common factor number is the GCF number.
So the greatest common factor 48090 and 48100 is 10.

Also check out the Least Common Multiple of 48090 and 48100