What is the Greatest Common Factor of 71728 and 71740?

Greatest common factor (GCF) of 71728 and 71740 is 4.

GCF(71728,71740) = 4

We will now calculate the prime factors of 71728 and 71740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71728 and 71740.

How to find the GCF of 71728 and 71740?

We will first find the prime factorization of 71728 and 71740. After we will calculate the factors of 71728 and 71740 and find the biggest common factor number .

Step-1: Prime Factorization of 71728

Prime factors of 71728 are 2, 4483. Prime factorization of 71728 in exponential form is:

71728 = 2⁴ × 4483¹

Step-2: Prime Factorization of 71740

Prime factors of 71740 are 2, 5, 17, 211. Prime factorization of 71740 in exponential form is:

71740 = 2² × 5¹ × 17¹ × 211¹

Step-3: Factors of 71728

List of positive integer factors of 71728 that divides 71728 without a remainder.

1, 2, 4, 8, 16, 4483, 8966, 17932, 35864

Step-4: Factors of 71740

List of positive integer factors of 71740 that divides 71728 without a remainder.

1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 211, 340, 422, 844, 1055, 2110, 3587, 4220, 7174, 14348, 17935, 35870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71728 and 71740. The biggest common factor number is the GCF number.
So the greatest common factor 71728 and 71740 is 4.

Also check out the Least Common Multiple of 71728 and 71740