What is the Greatest Common Factor of 30753 and 30768?

Greatest common factor (GCF) of 30753 and 30768 is 3.

GCF(30753,30768) = 3

We will now calculate the prime factors of 30753 and 30768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30753 and 30768.

How to find the GCF of 30753 and 30768?

We will first find the prime factorization of 30753 and 30768. After we will calculate the factors of 30753 and 30768 and find the biggest common factor number .

Step-1: Prime Factorization of 30753

Prime factors of 30753 are 3, 17, 67. Prime factorization of 30753 in exponential form is:

30753 = 3³ × 17¹ × 67¹

Step-2: Prime Factorization of 30768

Prime factors of 30768 are 2, 3, 641. Prime factorization of 30768 in exponential form is:

30768 = 2⁴ × 3¹ × 641¹

Step-3: Factors of 30753

List of positive integer factors of 30753 that divides 30753 without a remainder.

1, 3, 9, 17, 27, 51, 67, 153, 201, 459, 603, 1139, 1809, 3417, 10251

Step-4: Factors of 30768

List of positive integer factors of 30768 that divides 30753 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 641, 1282, 1923, 2564, 3846, 5128, 7692, 10256, 15384

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30753 and 30768. The biggest common factor number is the GCF number.
So the greatest common factor 30753 and 30768 is 3.

Also check out the Least Common Multiple of 30753 and 30768