What is the Greatest Common Factor of 30960 and 30969?

Greatest common factor (GCF) of 30960 and 30969 is 9.

GCF(30960,30969) = 9

We will now calculate the prime factors of 30960 and 30969, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30960 and 30969.

How to find the GCF of 30960 and 30969?

We will first find the prime factorization of 30960 and 30969. After we will calculate the factors of 30960 and 30969 and find the biggest common factor number .

Step-1: Prime Factorization of 30960

Prime factors of 30960 are 2, 3, 5, 43. Prime factorization of 30960 in exponential form is:

30960 = 2⁴ × 3² × 5¹ × 43¹

Step-2: Prime Factorization of 30969

Prime factors of 30969 are 3, 31, 37. Prime factorization of 30969 in exponential form is:

30969 = 3³ × 31¹ × 37¹

Step-3: Factors of 30960

List of positive integer factors of 30960 that divides 30960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 43, 45, 48, 60, 72, 80, 86, 90, 120, 129, 144, 172, 180, 215, 240, 258, 344, 360, 387, 430, 516, 645, 688, 720, 774, 860, 1032, 1290, 1548, 1720, 1935, 2064, 2580, 3096, 3440, 3870, 5160, 6192, 7740, 10320, 15480

Step-4: Factors of 30969

List of positive integer factors of 30969 that divides 30960 without a remainder.

1, 3, 9, 27, 31, 37, 93, 111, 279, 333, 837, 999, 1147, 3441, 10323

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30960 and 30969. The biggest common factor number is the GCF number.
So the greatest common factor 30960 and 30969 is 9.

Also check out the Least Common Multiple of 30960 and 30969