What is the Greatest Common Factor of 75264 and 75270?

Greatest common factor (GCF) of 75264 and 75270 is 6.

GCF(75264,75270) = 6

We will now calculate the prime factors of 75264 and 75270, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75264 and 75270.

How to find the GCF of 75264 and 75270?

We will first find the prime factorization of 75264 and 75270. After we will calculate the factors of 75264 and 75270 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 75270

Prime factors of 75270 are 2, 3, 5, 13, 193. Prime factorization of 75270 in exponential form is:

75270 = 2¹ × 3¹ × 5¹ × 13¹ × 193¹

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 75270

List of positive integer factors of 75270 that divides 75264 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 193, 195, 386, 390, 579, 965, 1158, 1930, 2509, 2895, 5018, 5790, 7527, 12545, 15054, 25090, 37635

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75264 and 75270. The biggest common factor number is the GCF number.
So the greatest common factor 75264 and 75270 is 6.

Also check out the Least Common Multiple of 75264 and 75270