What is the Greatest Common Factor of 48208 and 48214?

Greatest common factor (GCF) of 48208 and 48214 is 2.

GCF(48208,48214) = 2

We will now calculate the prime factors of 48208 and 48214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48208 and 48214.

How to find the GCF of 48208 and 48214?

We will first find the prime factorization of 48208 and 48214. After we will calculate the factors of 48208 and 48214 and find the biggest common factor number .

Step-1: Prime Factorization of 48208

Prime factors of 48208 are 2, 23, 131. Prime factorization of 48208 in exponential form is:

48208 = 2⁴ × 23¹ × 131¹

Step-2: Prime Factorization of 48214

Prime factors of 48214 are 2, 24107. Prime factorization of 48214 in exponential form is:

48214 = 2¹ × 24107¹

Step-3: Factors of 48208

List of positive integer factors of 48208 that divides 48208 without a remainder.

1, 2, 4, 8, 16, 23, 46, 92, 131, 184, 262, 368, 524, 1048, 2096, 3013, 6026, 12052, 24104

Step-4: Factors of 48214

List of positive integer factors of 48214 that divides 48208 without a remainder.

1, 2, 24107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48208 and 48214. The biggest common factor number is the GCF number.
So the greatest common factor 48208 and 48214 is 2.

Also check out the Least Common Multiple of 48208 and 48214