What is the Greatest Common Factor of 30954 and 30960?

Greatest common factor (GCF) of 30954 and 30960 is 6.

GCF(30954,30960) = 6

We will now calculate the prime factors of 30954 and 30960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30954 and 30960.

How to find the GCF of 30954 and 30960?

We will first find the prime factorization of 30954 and 30960. After we will calculate the factors of 30954 and 30960 and find the biggest common factor number .

Step-1: Prime Factorization of 30954

Prime factors of 30954 are 2, 3, 7, 11, 67. Prime factorization of 30954 in exponential form is:

30954 = 2¹ × 3¹ × 7¹ × 11¹ × 67¹

Step-2: 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-3: Factors of 30954

List of positive integer factors of 30954 that divides 30954 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 67, 77, 134, 154, 201, 231, 402, 462, 469, 737, 938, 1407, 1474, 2211, 2814, 4422, 5159, 10318, 15477

Step-4: Factors of 30960

List of positive integer factors of 30960 that divides 30954 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30954 and 30960. The biggest common factor number is the GCF number.
So the greatest common factor 30954 and 30960 is 6.

Also check out the Least Common Multiple of 30954 and 30960