What is the Greatest Common Factor of 13950 and 13968?

Greatest common factor (GCF) of 13950 and 13968 is 18.

GCF(13950,13968) = 18

We will now calculate the prime factors of 13950 and 13968, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13950 and 13968.

How to find the GCF of 13950 and 13968?

We will first find the prime factorization of 13950 and 13968. After we will calculate the factors of 13950 and 13968 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13968

Prime factors of 13968 are 2, 3, 97. Prime factorization of 13968 in exponential form is:

13968 = 2⁴ × 3² × 97¹

Step-3: Factors of 13950

List of positive integer factors of 13950 that divides 13950 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

Step-4: Factors of 13968

List of positive integer factors of 13968 that divides 13950 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 97, 144, 194, 291, 388, 582, 776, 873, 1164, 1552, 1746, 2328, 3492, 4656, 6984

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13950 and 13968. The biggest common factor number is the GCF number.
So the greatest common factor 13950 and 13968 is 18.

Also check out the Least Common Multiple of 13950 and 13968