What is the Greatest Common Factor of 71664 and 71680?

Greatest common factor (GCF) of 71664 and 71680 is 16.

GCF(71664,71680) = 16

We will now calculate the prime factors of 71664 and 71680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71664 and 71680.

How to find the GCF of 71664 and 71680?

We will first find the prime factorization of 71664 and 71680. After we will calculate the factors of 71664 and 71680 and find the biggest common factor number .

Step-1: Prime Factorization of 71664

Prime factors of 71664 are 2, 3, 1493. Prime factorization of 71664 in exponential form is:

71664 = 2⁴ × 3¹ × 1493¹

Step-2: Prime Factorization of 71680

Prime factors of 71680 are 2, 5, 7. Prime factorization of 71680 in exponential form is:

71680 = 2¹¹ × 5¹ × 7¹

Step-3: Factors of 71664

List of positive integer factors of 71664 that divides 71664 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1493, 2986, 4479, 5972, 8958, 11944, 17916, 23888, 35832

Step-4: Factors of 71680

List of positive integer factors of 71680 that divides 71664 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 128, 140, 160, 224, 256, 280, 320, 448, 512, 560, 640, 896, 1024, 1120, 1280, 1792, 2048, 2240, 2560, 3584, 4480, 5120, 7168, 8960, 10240, 14336, 17920, 35840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71664 and 71680. The biggest common factor number is the GCF number.
So the greatest common factor 71664 and 71680 is 16.

Also check out the Least Common Multiple of 71664 and 71680