What is the Greatest Common Factor of 13944 and 13964?

Greatest common factor (GCF) of 13944 and 13964 is 4.

GCF(13944,13964) = 4

We will now calculate the prime factors of 13944 and 13964, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13944 and 13964.

How to find the GCF of 13944 and 13964?

We will first find the prime factorization of 13944 and 13964. After we will calculate the factors of 13944 and 13964 and find the biggest common factor number .

Step-1: Prime Factorization of 13944

Prime factors of 13944 are 2, 3, 7, 83. Prime factorization of 13944 in exponential form is:

13944 = 2³ × 3¹ × 7¹ × 83¹

Step-2: Prime Factorization of 13964

Prime factors of 13964 are 2, 3491. Prime factorization of 13964 in exponential form is:

13964 = 2² × 3491¹

Step-3: Factors of 13944

List of positive integer factors of 13944 that divides 13944 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 83, 84, 166, 168, 249, 332, 498, 581, 664, 996, 1162, 1743, 1992, 2324, 3486, 4648, 6972

Step-4: Factors of 13964

List of positive integer factors of 13964 that divides 13944 without a remainder.

1, 2, 4, 3491, 6982

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13944 and 13964. The biggest common factor number is the GCF number.
So the greatest common factor 13944 and 13964 is 4.

Also check out the Least Common Multiple of 13944 and 13964