What is the Greatest Common Factor of 75264 and 75278?

Greatest common factor (GCF) of 75264 and 75278 is 14.

GCF(75264,75278) = 14

We will now calculate the prime factors of 75264 and 75278, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75264 and 75278.

How to find the GCF of 75264 and 75278?

We will first find the prime factorization of 75264 and 75278. After we will calculate the factors of 75264 and 75278 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 75278

Prime factors of 75278 are 2, 7, 19, 283. Prime factorization of 75278 in exponential form is:

75278 = 2¹ × 7¹ × 19¹ × 283¹

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 75278

List of positive integer factors of 75278 that divides 75264 without a remainder.

1, 2, 7, 14, 19, 38, 133, 266, 283, 566, 1981, 3962, 5377, 10754, 37639

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75264 and 75278. The biggest common factor number is the GCF number.
So the greatest common factor 75264 and 75278 is 14.

Also check out the Least Common Multiple of 75264 and 75278