What is the Greatest Common Factor of 67760 and 67774?

Greatest common factor (GCF) of 67760 and 67774 is 14.

GCF(67760,67774) = 14

We will now calculate the prime factors of 67760 and 67774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67760 and 67774.

How to find the GCF of 67760 and 67774?

We will first find the prime factorization of 67760 and 67774. After we will calculate the factors of 67760 and 67774 and find the biggest common factor number .

Step-1: Prime Factorization of 67760

Prime factors of 67760 are 2, 5, 7, 11. Prime factorization of 67760 in exponential form is:

67760 = 2⁴ × 5¹ × 7¹ × 11²

Step-2: Prime Factorization of 67774

Prime factors of 67774 are 2, 7, 47, 103. Prime factorization of 67774 in exponential form is:

67774 = 2¹ × 7¹ × 47¹ × 103¹

Step-3: Factors of 67760

List of positive integer factors of 67760 that divides 67760 without a remainder.

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 20, 22, 28, 35, 40, 44, 55, 56, 70, 77, 80, 88, 110, 112, 121, 140, 154, 176, 220, 242, 280, 308, 385, 440, 484, 560, 605, 616, 770, 847, 880, 968, 1210, 1232, 1540, 1694, 1936, 2420, 3080, 3388, 4235, 4840, 6160, 6776, 8470, 9680, 13552, 16940, 33880

Step-4: Factors of 67774

List of positive integer factors of 67774 that divides 67760 without a remainder.

1, 2, 7, 14, 47, 94, 103, 206, 329, 658, 721, 1442, 4841, 9682, 33887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67760 and 67774. The biggest common factor number is the GCF number.
So the greatest common factor 67760 and 67774 is 14.

Also check out the Least Common Multiple of 67760 and 67774