What is the Greatest Common Factor of 48400 and 48415?

Greatest common factor (GCF) of 48400 and 48415 is 5.

GCF(48400,48415) = 5

We will now calculate the prime factors of 48400 and 48415, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48400 and 48415.

How to find the GCF of 48400 and 48415?

We will first find the prime factorization of 48400 and 48415. After we will calculate the factors of 48400 and 48415 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 48415

Prime factors of 48415 are 5, 23, 421. Prime factorization of 48415 in exponential form is:

48415 = 5¹ × 23¹ × 421¹

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 48415

List of positive integer factors of 48415 that divides 48400 without a remainder.

1, 5, 23, 115, 421, 2105, 9683

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48400 and 48415. The biggest common factor number is the GCF number.
So the greatest common factor 48400 and 48415 is 5.

Also check out the Least Common Multiple of 48400 and 48415