What is the Greatest Common Factor of 49952 and 49972?

Greatest common factor (GCF) of 49952 and 49972 is 4.

GCF(49952,49972) = 4

We will now calculate the prime factors of 49952 and 49972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49952 and 49972.

How to find the GCF of 49952 and 49972?

We will first find the prime factorization of 49952 and 49972. After we will calculate the factors of 49952 and 49972 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 49972

Prime factors of 49972 are 2, 13, 31. Prime factorization of 49972 in exponential form is:

49972 = 2² × 13¹ × 31²

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 49972

List of positive integer factors of 49972 that divides 49952 without a remainder.

1, 2, 4, 13, 26, 31, 52, 62, 124, 403, 806, 961, 1612, 1922, 3844, 12493, 24986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49952 and 49972. The biggest common factor number is the GCF number.
So the greatest common factor 49952 and 49972 is 4.

Also check out the Least Common Multiple of 49952 and 49972