What is the Greatest Common Factor of 71675 and 71680?

Greatest common factor (GCF) of 71675 and 71680 is 5.

GCF(71675,71680) = 5

We will now calculate the prime factors of 71675 and 71680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71675 and 71680.

How to find the GCF of 71675 and 71680?

We will first find the prime factorization of 71675 and 71680. After we will calculate the factors of 71675 and 71680 and find the biggest common factor number .

Step-1: Prime Factorization of 71675

Prime factors of 71675 are 5, 47, 61. Prime factorization of 71675 in exponential form is:

71675 = 5² × 47¹ × 61¹

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 71675

List of positive integer factors of 71675 that divides 71675 without a remainder.

1, 5, 25, 47, 61, 235, 305, 1175, 1525, 2867, 14335

Step-4: Factors of 71680

List of positive integer factors of 71680 that divides 71675 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 71675 and 71680. The biggest common factor number is the GCF number.
So the greatest common factor 71675 and 71680 is 5.

Also check out the Least Common Multiple of 71675 and 71680