What is the Greatest Common Factor of 71328 and 71340?

Greatest common factor (GCF) of 71328 and 71340 is 12.

GCF(71328,71340) = 12

We will now calculate the prime factors of 71328 and 71340, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71328 and 71340.

How to find the GCF of 71328 and 71340?

We will first find the prime factorization of 71328 and 71340. After we will calculate the factors of 71328 and 71340 and find the biggest common factor number .

Step-1: Prime Factorization of 71328

Prime factors of 71328 are 2, 3, 743. Prime factorization of 71328 in exponential form is:

71328 = 2⁵ × 3¹ × 743¹

Step-2: Prime Factorization of 71340

Prime factors of 71340 are 2, 3, 5, 29, 41. Prime factorization of 71340 in exponential form is:

71340 = 2² × 3¹ × 5¹ × 29¹ × 41¹

Step-3: Factors of 71328

List of positive integer factors of 71328 that divides 71328 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 743, 1486, 2229, 2972, 4458, 5944, 8916, 11888, 17832, 23776, 35664

Step-4: Factors of 71340

List of positive integer factors of 71340 that divides 71328 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 41, 58, 60, 82, 87, 116, 123, 145, 164, 174, 205, 246, 290, 348, 410, 435, 492, 580, 615, 820, 870, 1189, 1230, 1740, 2378, 2460, 3567, 4756, 5945, 7134, 11890, 14268, 17835, 23780, 35670

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71328 and 71340. The biggest common factor number is the GCF number.
So the greatest common factor 71328 and 71340 is 12.

Also check out the Least Common Multiple of 71328 and 71340