What is the Greatest Common Factor of 54400 and 54417?

Greatest common factor (GCF) of 54400 and 54417 is 17.

GCF(54400,54417) = 17

We will now calculate the prime factors of 54400 and 54417, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54400 and 54417.

How to find the GCF of 54400 and 54417?

We will first find the prime factorization of 54400 and 54417. After we will calculate the factors of 54400 and 54417 and find the biggest common factor number .

Step-1: Prime Factorization of 54400

Prime factors of 54400 are 2, 5, 17. Prime factorization of 54400 in exponential form is:

54400 = 2⁷ × 5² × 17¹

Step-2: Prime Factorization of 54417

Prime factors of 54417 are 3, 11, 17, 97. Prime factorization of 54417 in exponential form is:

54417 = 3¹ × 11¹ × 17¹ × 97¹

Step-3: Factors of 54400

List of positive integer factors of 54400 that divides 54400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 64, 68, 80, 85, 100, 128, 136, 160, 170, 200, 272, 320, 340, 400, 425, 544, 640, 680, 800, 850, 1088, 1360, 1600, 1700, 2176, 2720, 3200, 3400, 5440, 6800, 10880, 13600, 27200

Step-4: Factors of 54417

List of positive integer factors of 54417 that divides 54400 without a remainder.

1, 3, 11, 17, 33, 51, 97, 187, 291, 561, 1067, 1649, 3201, 4947, 18139

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54400 and 54417. The biggest common factor number is the GCF number.
So the greatest common factor 54400 and 54417 is 17.

Also check out the Least Common Multiple of 54400 and 54417