What is the Greatest Common Factor of 71952 and 71968?

Greatest common factor (GCF) of 71952 and 71968 is 16.

GCF(71952,71968) = 16

We will now calculate the prime factors of 71952 and 71968, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71952 and 71968.

How to find the GCF of 71952 and 71968?

We will first find the prime factorization of 71952 and 71968. After we will calculate the factors of 71952 and 71968 and find the biggest common factor number .

Step-1: Prime Factorization of 71952

Prime factors of 71952 are 2, 3, 1499. Prime factorization of 71952 in exponential form is:

71952 = 2⁴ × 3¹ × 1499¹

Step-2: 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-3: Factors of 71952

List of positive integer factors of 71952 that divides 71952 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1499, 2998, 4497, 5996, 8994, 11992, 17988, 23984, 35976

Step-4: Factors of 71968

List of positive integer factors of 71968 that divides 71952 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71952 and 71968. The biggest common factor number is the GCF number.
So the greatest common factor 71952 and 71968 is 16.

Also check out the Least Common Multiple of 71952 and 71968