What is the Greatest Common Factor of 34749 and 34760?

Greatest common factor (GCF) of 34749 and 34760 is 11.

GCF(34749,34760) = 11

We will now calculate the prime factors of 34749 and 34760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34749 and 34760.

How to find the GCF of 34749 and 34760?

We will first find the prime factorization of 34749 and 34760. After we will calculate the factors of 34749 and 34760 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 34760

Prime factors of 34760 are 2, 5, 11, 79. Prime factorization of 34760 in exponential form is:

34760 = 2³ × 5¹ × 11¹ × 79¹

Step-3: Factors of 34749

List of positive integer factors of 34749 that divides 34749 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

Step-4: Factors of 34760

List of positive integer factors of 34760 that divides 34749 without a remainder.

1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 79, 88, 110, 158, 220, 316, 395, 440, 632, 790, 869, 1580, 1738, 3160, 3476, 4345, 6952, 8690, 17380

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34749 and 34760. The biggest common factor number is the GCF number.
So the greatest common factor 34749 and 34760 is 11.

Also check out the Least Common Multiple of 34749 and 34760