What is the Greatest Common Factor of 75264 and 75279?

Greatest common factor (GCF) of 75264 and 75279 is 3.

GCF(75264,75279) = 3

We will now calculate the prime factors of 75264 and 75279, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75264 and 75279.

How to find the GCF of 75264 and 75279?

We will first find the prime factorization of 75264 and 75279. After we will calculate the factors of 75264 and 75279 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 75279

Prime factors of 75279 are 3, 23, 1091. Prime factorization of 75279 in exponential form is:

75279 = 3¹ × 23¹ × 1091¹

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 75279

List of positive integer factors of 75279 that divides 75264 without a remainder.

1, 3, 23, 69, 1091, 3273, 25093

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75264 and 75279. The biggest common factor number is the GCF number.
So the greatest common factor 75264 and 75279 is 3.

Also check out the Least Common Multiple of 75264 and 75279