What is the Greatest Common Factor of 67744 and 67754?

Greatest common factor (GCF) of 67744 and 67754 is 2.

GCF(67744,67754) = 2

We will now calculate the prime factors of 67744 and 67754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67744 and 67754.

How to find the GCF of 67744 and 67754?

We will first find the prime factorization of 67744 and 67754. After we will calculate the factors of 67744 and 67754 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 67754

Prime factors of 67754 are 2, 19, 1783. Prime factorization of 67754 in exponential form is:

67754 = 2¹ × 19¹ × 1783¹

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 67754

List of positive integer factors of 67754 that divides 67744 without a remainder.

1, 2, 19, 38, 1783, 3566, 33877

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67744 and 67754. The biggest common factor number is the GCF number.
So the greatest common factor 67744 and 67754 is 2.

Also check out the Least Common Multiple of 67744 and 67754