What is the Greatest Common Factor of 75264 and 75280?

Greatest common factor (GCF) of 75264 and 75280 is 16.

GCF(75264,75280) = 16

We will now calculate the prime factors of 75264 and 75280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75264 and 75280.

How to find the GCF of 75264 and 75280?

We will first find the prime factorization of 75264 and 75280. After we will calculate the factors of 75264 and 75280 and find the biggest common factor number .

Step-1: Prime Factorization of 75264

Prime factors of 75264 are 2, 3, 7. Prime factorization of 75264 in exponential form is:

75264 = 2⁹ × 3¹ × 7²

Step-2: Prime Factorization of 75280

Prime factors of 75280 are 2, 5, 941. Prime factorization of 75280 in exponential form is:

75280 = 2⁴ × 5¹ × 941¹

Step-3: Factors of 75264

List of positive integer factors of 75264 that divides 75264 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 49, 56, 64, 84, 96, 98, 112, 128, 147, 168, 192, 196, 224, 256, 294, 336, 384, 392, 448, 512, 588, 672, 768, 784, 896, 1176, 1344, 1536, 1568, 1792, 2352, 2688, 3136, 3584, 4704, 5376, 6272, 9408, 10752, 12544, 18816, 25088, 37632

Step-4: Factors of 75280

List of positive integer factors of 75280 that divides 75264 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 941, 1882, 3764, 4705, 7528, 9410, 15056, 18820, 37640

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75264 and 75280. The biggest common factor number is the GCF number.
So the greatest common factor 75264 and 75280 is 16.

Also check out the Least Common Multiple of 75264 and 75280