What is the Greatest Common Factor of 34749 and 34758?

Greatest common factor (GCF) of 34749 and 34758 is 9.

GCF(34749,34758) = 9

We will now calculate the prime factors of 34749 and 34758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34749 and 34758.

How to find the GCF of 34749 and 34758?

We will first find the prime factorization of 34749 and 34758. After we will calculate the factors of 34749 and 34758 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 34758

Prime factors of 34758 are 2, 3, 1931. Prime factorization of 34758 in exponential form is:

34758 = 2¹ × 3² × 1931¹

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 34758

List of positive integer factors of 34758 that divides 34749 without a remainder.

1, 2, 3, 6, 9, 18, 1931, 3862, 5793, 11586, 17379

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34749 and 34758. The biggest common factor number is the GCF number.
So the greatest common factor 34749 and 34758 is 9.

Also check out the Least Common Multiple of 34749 and 34758