What is the Greatest Common Factor of 67734 and 67749?

Greatest common factor (GCF) of 67734 and 67749 is 3.

GCF(67734,67749) = 3

We will now calculate the prime factors of 67734 and 67749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67734 and 67749.

How to find the GCF of 67734 and 67749?

We will first find the prime factorization of 67734 and 67749. After we will calculate the factors of 67734 and 67749 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 67749

Prime factors of 67749 are 3, 11, 2053. Prime factorization of 67749 in exponential form is:

67749 = 3¹ × 11¹ × 2053¹

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 67749

List of positive integer factors of 67749 that divides 67734 without a remainder.

1, 3, 11, 33, 2053, 6159, 22583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67734 and 67749. The biggest common factor number is the GCF number.
So the greatest common factor 67734 and 67749 is 3.

Also check out the Least Common Multiple of 67734 and 67749