What is the Greatest Common Factor of 71680 and 71700?

Greatest common factor (GCF) of 71680 and 71700 is 20.

GCF(71680,71700) = 20

We will now calculate the prime factors of 71680 and 71700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71680 and 71700.

How to find the GCF of 71680 and 71700?

We will first find the prime factorization of 71680 and 71700. After we will calculate the factors of 71680 and 71700 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 71700

Prime factors of 71700 are 2, 3, 5, 239. Prime factorization of 71700 in exponential form is:

71700 = 2² × 3¹ × 5² × 239¹

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 71700

List of positive integer factors of 71700 that divides 71680 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 239, 300, 478, 717, 956, 1195, 1434, 2390, 2868, 3585, 4780, 5975, 7170, 11950, 14340, 17925, 23900, 35850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71680 and 71700. The biggest common factor number is the GCF number.
So the greatest common factor 71680 and 71700 is 20.

Also check out the Least Common Multiple of 71680 and 71700