What is the Greatest Common Factor of 67744 and 67760?

Greatest common factor (GCF) of 67744 and 67760 is 16.

GCF(67744,67760) = 16

We will now calculate the prime factors of 67744 and 67760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67744 and 67760.

How to find the GCF of 67744 and 67760?

We will first find the prime factorization of 67744 and 67760. After we will calculate the factors of 67744 and 67760 and find the biggest common factor number .

Step-1: Prime Factorization of 67744

Prime factors of 67744 are 2, 29, 73. Prime factorization of 67744 in exponential form is:

67744 = 2⁵ × 29¹ × 73¹

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 67744

List of positive integer factors of 67744 that divides 67744 without a remainder.

1, 2, 4, 8, 16, 29, 32, 58, 73, 116, 146, 232, 292, 464, 584, 928, 1168, 2117, 2336, 4234, 8468, 16936, 33872

Step-4: Factors of 67760

List of positive integer factors of 67760 that divides 67744 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 67744 and 67760. The biggest common factor number is the GCF number.
So the greatest common factor 67744 and 67760 is 16.

Also check out the Least Common Multiple of 67744 and 67760