What is the Greatest Common Factor of 49952 and 49966?

Greatest common factor (GCF) of 49952 and 49966 is 14.

GCF(49952,49966) = 14

We will now calculate the prime factors of 49952 and 49966, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49952 and 49966.

How to find the GCF of 49952 and 49966?

We will first find the prime factorization of 49952 and 49966. After we will calculate the factors of 49952 and 49966 and find the biggest common factor number .

Step-1: Prime Factorization of 49952

Prime factors of 49952 are 2, 7, 223. Prime factorization of 49952 in exponential form is:

49952 = 2⁵ × 7¹ × 223¹

Step-2: Prime Factorization of 49966

Prime factors of 49966 are 2, 7, 43, 83. Prime factorization of 49966 in exponential form is:

49966 = 2¹ × 7¹ × 43¹ × 83¹

Step-3: Factors of 49952

List of positive integer factors of 49952 that divides 49952 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 223, 224, 446, 892, 1561, 1784, 3122, 3568, 6244, 7136, 12488, 24976

Step-4: Factors of 49966

List of positive integer factors of 49966 that divides 49952 without a remainder.

1, 2, 7, 14, 43, 83, 86, 166, 301, 581, 602, 1162, 3569, 7138, 24983

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49952 and 49966. The biggest common factor number is the GCF number.
So the greatest common factor 49952 and 49966 is 14.

Also check out the Least Common Multiple of 49952 and 49966