What is the Greatest Common Factor of 6258 and 6272?

Greatest common factor (GCF) of 6258 and 6272 is 14.

GCF(6258,6272) = 14

We will now calculate the prime factors of 6258 and 6272, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6258 and 6272.

How to find the GCF of 6258 and 6272?

We will first find the prime factorization of 6258 and 6272. After we will calculate the factors of 6258 and 6272 and find the biggest common factor number .

Step-1: Prime Factorization of 6258

Prime factors of 6258 are 2, 3, 7, 149. Prime factorization of 6258 in exponential form is:

6258 = 2¹ × 3¹ × 7¹ × 149¹

Step-2: Prime Factorization of 6272

Prime factors of 6272 are 2, 7. Prime factorization of 6272 in exponential form is:

6272 = 2⁷ × 7²

Step-3: Factors of 6258

List of positive integer factors of 6258 that divides 6258 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 149, 298, 447, 894, 1043, 2086, 3129

Step-4: Factors of 6272

List of positive integer factors of 6272 that divides 6258 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 128, 196, 224, 392, 448, 784, 896, 1568, 3136

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6258 and 6272. The biggest common factor number is the GCF number.
So the greatest common factor 6258 and 6272 is 14.

Also check out the Least Common Multiple of 6258 and 6272