What is the Greatest Common Factor of 67734 and 67744?

Greatest common factor (GCF) of 67734 and 67744 is 2.

GCF(67734,67744) = 2

We will now calculate the prime factors of 67734 and 67744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67734 and 67744.

How to find the GCF of 67734 and 67744?

We will first find the prime factorization of 67734 and 67744. After we will calculate the factors of 67734 and 67744 and find the biggest common factor number .

Step-1: Prime Factorization of 67734

Prime factors of 67734 are 2, 3, 53, 71. Prime factorization of 67734 in exponential form is:

67734 = 2¹ × 3² × 53¹ × 71¹

Step-2: 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-3: Factors of 67734

List of positive integer factors of 67734 that divides 67734 without a remainder.

1, 2, 3, 6, 9, 18, 53, 71, 106, 142, 159, 213, 318, 426, 477, 639, 954, 1278, 3763, 7526, 11289, 22578, 33867

Step-4: Factors of 67744

List of positive integer factors of 67744 that divides 67734 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67734 and 67744. The biggest common factor number is the GCF number.
So the greatest common factor 67734 and 67744 is 2.

Also check out the Least Common Multiple of 67734 and 67744