What is the Greatest Common Factor of 13952 and 13970?

Greatest common factor (GCF) of 13952 and 13970 is 2.

GCF(13952,13970) = 2

We will now calculate the prime factors of 13952 and 13970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13952 and 13970.

How to find the GCF of 13952 and 13970?

We will first find the prime factorization of 13952 and 13970. After we will calculate the factors of 13952 and 13970 and find the biggest common factor number .

Step-1: Prime Factorization of 13952

Prime factors of 13952 are 2, 109. Prime factorization of 13952 in exponential form is:

13952 = 2⁷ × 109¹

Step-2: Prime Factorization of 13970

Prime factors of 13970 are 2, 5, 11, 127. Prime factorization of 13970 in exponential form is:

13970 = 2¹ × 5¹ × 11¹ × 127¹

Step-3: Factors of 13952

List of positive integer factors of 13952 that divides 13952 without a remainder.

1, 2, 4, 8, 16, 32, 64, 109, 128, 218, 436, 872, 1744, 3488, 6976

Step-4: Factors of 13970

List of positive integer factors of 13970 that divides 13952 without a remainder.

1, 2, 5, 10, 11, 22, 55, 110, 127, 254, 635, 1270, 1397, 2794, 6985

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13952 and 13970. The biggest common factor number is the GCF number.
So the greatest common factor 13952 and 13970 is 2.

Also check out the Least Common Multiple of 13952 and 13970