What is the Greatest Common Factor of 30738 and 30744?

Greatest common factor (GCF) of 30738 and 30744 is 6.

GCF(30738,30744) = 6

We will now calculate the prime factors of 30738 and 30744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30738 and 30744.

How to find the GCF of 30738 and 30744?

We will first find the prime factorization of 30738 and 30744. After we will calculate the factors of 30738 and 30744 and find the biggest common factor number .

Step-1: Prime Factorization of 30738

Prime factors of 30738 are 2, 3, 47, 109. Prime factorization of 30738 in exponential form is:

30738 = 2¹ × 3¹ × 47¹ × 109¹

Step-2: Prime Factorization of 30744

Prime factors of 30744 are 2, 3, 7, 61. Prime factorization of 30744 in exponential form is:

30744 = 2³ × 3² × 7¹ × 61¹

Step-3: Factors of 30738

List of positive integer factors of 30738 that divides 30738 without a remainder.

1, 2, 3, 6, 47, 94, 109, 141, 218, 282, 327, 654, 5123, 10246, 15369

Step-4: Factors of 30744

List of positive integer factors of 30744 that divides 30738 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 61, 63, 72, 84, 122, 126, 168, 183, 244, 252, 366, 427, 488, 504, 549, 732, 854, 1098, 1281, 1464, 1708, 2196, 2562, 3416, 3843, 4392, 5124, 7686, 10248, 15372

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30738 and 30744. The biggest common factor number is the GCF number.
So the greatest common factor 30738 and 30744 is 6.

Also check out the Least Common Multiple of 30738 and 30744