What is the Greatest Common Factor of 75250 and 75264?

Greatest common factor (GCF) of 75250 and 75264 is 14.

GCF(75250,75264) = 14

We will now calculate the prime factors of 75250 and 75264, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75250 and 75264.

How to find the GCF of 75250 and 75264?

We will first find the prime factorization of 75250 and 75264. After we will calculate the factors of 75250 and 75264 and find the biggest common factor number .

Step-1: Prime Factorization of 75250

Prime factors of 75250 are 2, 5, 7, 43. Prime factorization of 75250 in exponential form is:

75250 = 2¹ × 5³ × 7¹ × 43¹

Step-2: 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-3: Factors of 75250

List of positive integer factors of 75250 that divides 75250 without a remainder.

1, 2, 5, 7, 10, 14, 25, 35, 43, 50, 70, 86, 125, 175, 215, 250, 301, 350, 430, 602, 875, 1075, 1505, 1750, 2150, 3010, 5375, 7525, 10750, 15050, 37625

Step-4: Factors of 75264

List of positive integer factors of 75264 that divides 75250 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75250 and 75264. The biggest common factor number is the GCF number.
So the greatest common factor 75250 and 75264 is 14.

Also check out the Least Common Multiple of 75250 and 75264