What is the Greatest Common Factor of 25214 and 25228?

Greatest common factor (GCF) of 25214 and 25228 is 14.

GCF(25214,25228) = 14

We will now calculate the prime factors of 25214 and 25228, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25214 and 25228.

How to find the GCF of 25214 and 25228?

We will first find the prime factorization of 25214 and 25228. After we will calculate the factors of 25214 and 25228 and find the biggest common factor number .

Step-1: Prime Factorization of 25214

Prime factors of 25214 are 2, 7, 1801. Prime factorization of 25214 in exponential form is:

25214 = 2¹ × 7¹ × 1801¹

Step-2: Prime Factorization of 25228

Prime factors of 25228 are 2, 7, 17, 53. Prime factorization of 25228 in exponential form is:

25228 = 2² × 7¹ × 17¹ × 53¹

Step-3: Factors of 25214

List of positive integer factors of 25214 that divides 25214 without a remainder.

1, 2, 7, 14, 1801, 3602, 12607

Step-4: Factors of 25228

List of positive integer factors of 25228 that divides 25214 without a remainder.

1, 2, 4, 7, 14, 17, 28, 34, 53, 68, 106, 119, 212, 238, 371, 476, 742, 901, 1484, 1802, 3604, 6307, 12614

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25214 and 25228. The biggest common factor number is the GCF number.
So the greatest common factor 25214 and 25228 is 14.

Also check out the Least Common Multiple of 25214 and 25228