What is the Greatest Common Factor of 13944 and 13950?

Greatest common factor (GCF) of 13944 and 13950 is 6.

GCF(13944,13950) = 6

We will now calculate the prime factors of 13944 and 13950, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13944 and 13950.

How to find the GCF of 13944 and 13950?

We will first find the prime factorization of 13944 and 13950. After we will calculate the factors of 13944 and 13950 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 13950

Prime factors of 13950 are 2, 3, 5, 31. Prime factorization of 13950 in exponential form is:

13950 = 2¹ × 3² × 5² × 31¹

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 13950

List of positive integer factors of 13950 that divides 13944 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 31, 45, 50, 62, 75, 90, 93, 150, 155, 186, 225, 279, 310, 450, 465, 558, 775, 930, 1395, 1550, 2325, 2790, 4650, 6975

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13944 and 13950. The biggest common factor number is the GCF number.
So the greatest common factor 13944 and 13950 is 6.

Also check out the Least Common Multiple of 13944 and 13950