What is the Greatest Common Factor of 48400 and 48420?

Greatest common factor (GCF) of 48400 and 48420 is 20.

GCF(48400,48420) = 20

We will now calculate the prime factors of 48400 and 48420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48400 and 48420.

How to find the GCF of 48400 and 48420?

We will first find the prime factorization of 48400 and 48420. After we will calculate the factors of 48400 and 48420 and find the biggest common factor number .

Step-1: Prime Factorization of 48400

Prime factors of 48400 are 2, 5, 11. Prime factorization of 48400 in exponential form is:

48400 = 2⁴ × 5² × 11²

Step-2: Prime Factorization of 48420

Prime factors of 48420 are 2, 3, 5, 269. Prime factorization of 48420 in exponential form is:

48420 = 2² × 3² × 5¹ × 269¹

Step-3: Factors of 48400

List of positive integer factors of 48400 that divides 48400 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 40, 44, 50, 55, 80, 88, 100, 110, 121, 176, 200, 220, 242, 275, 400, 440, 484, 550, 605, 880, 968, 1100, 1210, 1936, 2200, 2420, 3025, 4400, 4840, 6050, 9680, 12100, 24200

Step-4: Factors of 48420

List of positive integer factors of 48420 that divides 48400 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 269, 538, 807, 1076, 1345, 1614, 2421, 2690, 3228, 4035, 4842, 5380, 8070, 9684, 12105, 16140, 24210

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48400 and 48420. The biggest common factor number is the GCF number.
So the greatest common factor 48400 and 48420 is 20.

Also check out the Least Common Multiple of 48400 and 48420