What is the Greatest Common Factor of 34738 and 34749?

Greatest common factor (GCF) of 34738 and 34749 is 11.

GCF(34738,34749) = 11

We will now calculate the prime factors of 34738 and 34749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34738 and 34749.

How to find the GCF of 34738 and 34749?

We will first find the prime factorization of 34738 and 34749. After we will calculate the factors of 34738 and 34749 and find the biggest common factor number .

Step-1: Prime Factorization of 34738

Prime factors of 34738 are 2, 11, 1579. Prime factorization of 34738 in exponential form is:

34738 = 2¹ × 11¹ × 1579¹

Step-2: Prime Factorization of 34749

Prime factors of 34749 are 3, 11, 13. Prime factorization of 34749 in exponential form is:

34749 = 3⁵ × 11¹ × 13¹

Step-3: Factors of 34738

List of positive integer factors of 34738 that divides 34738 without a remainder.

1, 2, 11, 22, 1579, 3158, 17369

Step-4: Factors of 34749

List of positive integer factors of 34749 that divides 34738 without a remainder.

1, 3, 9, 11, 13, 27, 33, 39, 81, 99, 117, 143, 243, 297, 351, 429, 891, 1053, 1287, 2673, 3159, 3861, 11583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34738 and 34749. The biggest common factor number is the GCF number.
So the greatest common factor 34738 and 34749 is 11.

Also check out the Least Common Multiple of 34738 and 34749