What is the Greatest Common Factor of 54400 and 54416?

Greatest common factor (GCF) of 54400 and 54416 is 16.

GCF(54400,54416) = 16

We will now calculate the prime factors of 54400 and 54416, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54400 and 54416.

How to find the GCF of 54400 and 54416?

We will first find the prime factorization of 54400 and 54416. After we will calculate the factors of 54400 and 54416 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 54416

Prime factors of 54416 are 2, 19, 179. Prime factorization of 54416 in exponential form is:

54416 = 2⁴ × 19¹ × 179¹

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 54416

List of positive integer factors of 54416 that divides 54400 without a remainder.

1, 2, 4, 8, 16, 19, 38, 76, 152, 179, 304, 358, 716, 1432, 2864, 3401, 6802, 13604, 27208

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54400 and 54416. The biggest common factor number is the GCF number.
So the greatest common factor 54400 and 54416 is 16.

Also check out the Least Common Multiple of 54400 and 54416