What is the Greatest Common Factor of 30360 and 30378?

Greatest common factor (GCF) of 30360 and 30378 is 6.

GCF(30360,30378) = 6

We will now calculate the prime factors of 30360 and 30378, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30360 and 30378.

How to find the GCF of 30360 and 30378?

We will first find the prime factorization of 30360 and 30378. After we will calculate the factors of 30360 and 30378 and find the biggest common factor number .

Step-1: Prime Factorization of 30360

Prime factors of 30360 are 2, 3, 5, 11, 23. Prime factorization of 30360 in exponential form is:

30360 = 2³ × 3¹ × 5¹ × 11¹ × 23¹

Step-2: Prime Factorization of 30378

Prime factors of 30378 are 2, 3, 61, 83. Prime factorization of 30378 in exponential form is:

30378 = 2¹ × 3¹ × 61¹ × 83¹

Step-3: Factors of 30360

List of positive integer factors of 30360 that divides 30360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 23, 24, 30, 33, 40, 44, 46, 55, 60, 66, 69, 88, 92, 110, 115, 120, 132, 138, 165, 184, 220, 230, 253, 264, 276, 330, 345, 440, 460, 506, 552, 660, 690, 759, 920, 1012, 1265, 1320, 1380, 1518, 2024, 2530, 2760, 3036, 3795, 5060, 6072, 7590, 10120, 15180

Step-4: Factors of 30378

List of positive integer factors of 30378 that divides 30360 without a remainder.

1, 2, 3, 6, 61, 83, 122, 166, 183, 249, 366, 498, 5063, 10126, 15189

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30360 and 30378. The biggest common factor number is the GCF number.
So the greatest common factor 30360 and 30378 is 6.

Also check out the Least Common Multiple of 30360 and 30378