What is the Greatest Common Factor of 34736 and 34749?

Greatest common factor (GCF) of 34736 and 34749 is 13.

GCF(34736,34749) = 13

We will now calculate the prime factors of 34736 and 34749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34736 and 34749.

How to find the GCF of 34736 and 34749?

We will first find the prime factorization of 34736 and 34749. After we will calculate the factors of 34736 and 34749 and find the biggest common factor number .

Step-1: Prime Factorization of 34736

Prime factors of 34736 are 2, 13, 167. Prime factorization of 34736 in exponential form is:

34736 = 2⁴ × 13¹ × 167¹

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 34736

List of positive integer factors of 34736 that divides 34736 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 167, 208, 334, 668, 1336, 2171, 2672, 4342, 8684, 17368

Step-4: Factors of 34749

List of positive integer factors of 34749 that divides 34736 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 34736 and 34749. The biggest common factor number is the GCF number.
So the greatest common factor 34736 and 34749 is 13.

Also check out the Least Common Multiple of 34736 and 34749