What is the Greatest Common Factor of 71680 and 71690?

Greatest common factor (GCF) of 71680 and 71690 is 10.

GCF(71680,71690) = 10

We will now calculate the prime factors of 71680 and 71690, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71680 and 71690.

How to find the GCF of 71680 and 71690?

We will first find the prime factorization of 71680 and 71690. After we will calculate the factors of 71680 and 71690 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 71690

Prime factors of 71690 are 2, 5, 67, 107. Prime factorization of 71690 in exponential form is:

71690 = 2¹ × 5¹ × 67¹ × 107¹

Step-3: Factors of 71680

List of positive integer factors of 71680 that divides 71680 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

Step-4: Factors of 71690

List of positive integer factors of 71690 that divides 71680 without a remainder.

1, 2, 5, 10, 67, 107, 134, 214, 335, 535, 670, 1070, 7169, 14338, 35845

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71680 and 71690. The biggest common factor number is the GCF number.
So the greatest common factor 71680 and 71690 is 10.

Also check out the Least Common Multiple of 71680 and 71690