What is the Greatest Common Factor of 13874 and 13888?

Greatest common factor (GCF) of 13874 and 13888 is 14.

GCF(13874,13888) = 14

We will now calculate the prime factors of 13874 and 13888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13874 and 13888.

How to find the GCF of 13874 and 13888?

We will first find the prime factorization of 13874 and 13888. After we will calculate the factors of 13874 and 13888 and find the biggest common factor number .

Step-1: Prime Factorization of 13874

Prime factors of 13874 are 2, 7, 991. Prime factorization of 13874 in exponential form is:

13874 = 2¹ × 7¹ × 991¹

Step-2: Prime Factorization of 13888

Prime factors of 13888 are 2, 7, 31. Prime factorization of 13888 in exponential form is:

13888 = 2⁶ × 7¹ × 31¹

Step-3: Factors of 13874

List of positive integer factors of 13874 that divides 13874 without a remainder.

1, 2, 7, 14, 991, 1982, 6937

Step-4: Factors of 13888

List of positive integer factors of 13888 that divides 13874 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 31, 32, 56, 62, 64, 112, 124, 217, 224, 248, 434, 448, 496, 868, 992, 1736, 1984, 3472, 6944

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13874 and 13888. The biggest common factor number is the GCF number.
So the greatest common factor 13874 and 13888 is 14.

Also check out the Least Common Multiple of 13874 and 13888