What is the Greatest Common Factor of 30960 and 30978?

Greatest common factor (GCF) of 30960 and 30978 is 18.

GCF(30960,30978) = 18

We will now calculate the prime factors of 30960 and 30978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30960 and 30978.

How to find the GCF of 30960 and 30978?

We will first find the prime factorization of 30960 and 30978. After we will calculate the factors of 30960 and 30978 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 30978

Prime factors of 30978 are 2, 3, 1721. Prime factorization of 30978 in exponential form is:

30978 = 2¹ × 3² × 1721¹

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 30978

List of positive integer factors of 30978 that divides 30960 without a remainder.

1, 2, 3, 6, 9, 18, 1721, 3442, 5163, 10326, 15489

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30960 and 30978. The biggest common factor number is the GCF number.
So the greatest common factor 30960 and 30978 is 18.

Also check out the Least Common Multiple of 30960 and 30978