What is the Greatest Common Factor of 30351 and 30360?

Greatest common factor (GCF) of 30351 and 30360 is 3.

GCF(30351,30360) = 3

We will now calculate the prime factors of 30351 and 30360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30351 and 30360.

How to find the GCF of 30351 and 30360?

We will first find the prime factorization of 30351 and 30360. After we will calculate the factors of 30351 and 30360 and find the biggest common factor number .

Step-1: Prime Factorization of 30351

Prime factors of 30351 are 3, 67, 151. Prime factorization of 30351 in exponential form is:

30351 = 3¹ × 67¹ × 151¹

Step-2: 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-3: Factors of 30351

List of positive integer factors of 30351 that divides 30351 without a remainder.

1, 3, 67, 151, 201, 453, 10117

Step-4: Factors of 30360

List of positive integer factors of 30360 that divides 30351 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30351 and 30360. The biggest common factor number is the GCF number.
So the greatest common factor 30351 and 30360 is 3.

Also check out the Least Common Multiple of 30351 and 30360