What is the Greatest Common Factor of 67746 and 67760?

Greatest common factor (GCF) of 67746 and 67760 is 14.

GCF(67746,67760) = 14

We will now calculate the prime factors of 67746 and 67760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67746 and 67760.

How to find the GCF of 67746 and 67760?

We will first find the prime factorization of 67746 and 67760. After we will calculate the factors of 67746 and 67760 and find the biggest common factor number .

Step-1: Prime Factorization of 67746

Prime factors of 67746 are 2, 3, 7, 1613. Prime factorization of 67746 in exponential form is:

67746 = 2¹ × 3¹ × 7¹ × 1613¹

Step-2: 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-3: Factors of 67746

List of positive integer factors of 67746 that divides 67746 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1613, 3226, 4839, 9678, 11291, 22582, 33873

Step-4: Factors of 67760

List of positive integer factors of 67760 that divides 67746 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67746 and 67760. The biggest common factor number is the GCF number.
So the greatest common factor 67746 and 67760 is 14.

Also check out the Least Common Multiple of 67746 and 67760