What is the Greatest Common Factor of 30345 and 30352?

Greatest common factor (GCF) of 30345 and 30352 is 7.

GCF(30345,30352) = 7

We will now calculate the prime factors of 30345 and 30352, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30345 and 30352.

How to find the GCF of 30345 and 30352?

We will first find the prime factorization of 30345 and 30352. After we will calculate the factors of 30345 and 30352 and find the biggest common factor number .

Step-1: Prime Factorization of 30345

Prime factors of 30345 are 3, 5, 7, 17. Prime factorization of 30345 in exponential form is:

30345 = 3¹ × 5¹ × 7¹ × 17²

Step-2: Prime Factorization of 30352

Prime factors of 30352 are 2, 7, 271. Prime factorization of 30352 in exponential form is:

30352 = 2⁴ × 7¹ × 271¹

Step-3: Factors of 30345

List of positive integer factors of 30345 that divides 30345 without a remainder.

1, 3, 5, 7, 15, 17, 21, 35, 51, 85, 105, 119, 255, 289, 357, 595, 867, 1445, 1785, 2023, 4335, 6069, 10115

Step-4: Factors of 30352

List of positive integer factors of 30352 that divides 30345 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 271, 542, 1084, 1897, 2168, 3794, 4336, 7588, 15176

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30345 and 30352. The biggest common factor number is the GCF number.
So the greatest common factor 30345 and 30352 is 7.

Also check out the Least Common Multiple of 30345 and 30352