What is the Greatest Common Factor of 34965 and 34974?

Greatest common factor (GCF) of 34965 and 34974 is 9.

GCF(34965,34974) = 9

We will now calculate the prime factors of 34965 and 34974, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34965 and 34974.

How to find the GCF of 34965 and 34974?

We will first find the prime factorization of 34965 and 34974. After we will calculate the factors of 34965 and 34974 and find the biggest common factor number .

Step-1: Prime Factorization of 34965

Prime factors of 34965 are 3, 5, 7, 37. Prime factorization of 34965 in exponential form is:

34965 = 3³ × 5¹ × 7¹ × 37¹

Step-2: Prime Factorization of 34974

Prime factors of 34974 are 2, 3, 29, 67. Prime factorization of 34974 in exponential form is:

34974 = 2¹ × 3² × 29¹ × 67¹

Step-3: Factors of 34965

List of positive integer factors of 34965 that divides 34965 without a remainder.

1, 3, 5, 7, 9, 15, 21, 27, 35, 37, 45, 63, 105, 111, 135, 185, 189, 259, 315, 333, 555, 777, 945, 999, 1295, 1665, 2331, 3885, 4995, 6993, 11655

Step-4: Factors of 34974

List of positive integer factors of 34974 that divides 34965 without a remainder.

1, 2, 3, 6, 9, 18, 29, 58, 67, 87, 134, 174, 201, 261, 402, 522, 603, 1206, 1943, 3886, 5829, 11658, 17487

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34965 and 34974. The biggest common factor number is the GCF number.
So the greatest common factor 34965 and 34974 is 9.

Also check out the Least Common Multiple of 34965 and 34974