What is the Greatest Common Factor of 48400 and 48416?

Greatest common factor (GCF) of 48400 and 48416 is 16.

GCF(48400,48416) = 16

We will now calculate the prime factors of 48400 and 48416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48400 and 48416.

How to find the GCF of 48400 and 48416?

We will first find the prime factorization of 48400 and 48416. After we will calculate the factors of 48400 and 48416 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 48416

Prime factors of 48416 are 2, 17, 89. Prime factorization of 48416 in exponential form is:

48416 = 2⁵ × 17¹ × 89¹

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 48416

List of positive integer factors of 48416 that divides 48400 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 68, 89, 136, 178, 272, 356, 544, 712, 1424, 1513, 2848, 3026, 6052, 12104, 24208

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48400 and 48416. The biggest common factor number is the GCF number.
So the greatest common factor 48400 and 48416 is 16.

Also check out the Least Common Multiple of 48400 and 48416