What is the Greatest Common Factor of 34960 and 34965?

Greatest common factor (GCF) of 34960 and 34965 is 5.

GCF(34960,34965) = 5

We will now calculate the prime factors of 34960 and 34965, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34960 and 34965.

How to find the GCF of 34960 and 34965?

We will first find the prime factorization of 34960 and 34965. After we will calculate the factors of 34960 and 34965 and find the biggest common factor number .

Step-1: Prime Factorization of 34960

Prime factors of 34960 are 2, 5, 19, 23. Prime factorization of 34960 in exponential form is:

34960 = 2⁴ × 5¹ × 19¹ × 23¹

Step-2: 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-3: Factors of 34960

List of positive integer factors of 34960 that divides 34960 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 23, 38, 40, 46, 76, 80, 92, 95, 115, 152, 184, 190, 230, 304, 368, 380, 437, 460, 760, 874, 920, 1520, 1748, 1840, 2185, 3496, 4370, 6992, 8740, 17480

Step-4: Factors of 34965

List of positive integer factors of 34965 that divides 34960 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34960 and 34965. The biggest common factor number is the GCF number.
So the greatest common factor 34960 and 34965 is 5.

Also check out the Least Common Multiple of 34960 and 34965