What is the Greatest Common Factor of 71968 and 71972?

Greatest common factor (GCF) of 71968 and 71972 is 4.

GCF(71968,71972) = 4

We will now calculate the prime factors of 71968 and 71972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71968 and 71972.

How to find the GCF of 71968 and 71972?

We will first find the prime factorization of 71968 and 71972. After we will calculate the factors of 71968 and 71972 and find the biggest common factor number .

Step-1: Prime Factorization of 71968

Prime factors of 71968 are 2, 13, 173. Prime factorization of 71968 in exponential form is:

71968 = 2⁵ × 13¹ × 173¹

Step-2: Prime Factorization of 71972

Prime factors of 71972 are 2, 19, 947. Prime factorization of 71972 in exponential form is:

71972 = 2² × 19¹ × 947¹

Step-3: Factors of 71968

List of positive integer factors of 71968 that divides 71968 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 173, 208, 346, 416, 692, 1384, 2249, 2768, 4498, 5536, 8996, 17992, 35984

Step-4: Factors of 71972

List of positive integer factors of 71972 that divides 71968 without a remainder.

1, 2, 4, 19, 38, 76, 947, 1894, 3788, 17993, 35986

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71968 and 71972. The biggest common factor number is the GCF number.
So the greatest common factor 71968 and 71972 is 4.

Also check out the Least Common Multiple of 71968 and 71972