What is the Greatest Common Factor of 30744 and 30762?

Greatest common factor (GCF) of 30744 and 30762 is 18.

GCF(30744,30762) = 18

We will now calculate the prime factors of 30744 and 30762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30744 and 30762.

How to find the GCF of 30744 and 30762?

We will first find the prime factorization of 30744 and 30762. After we will calculate the factors of 30744 and 30762 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 30762

Prime factors of 30762 are 2, 3, 1709. Prime factorization of 30762 in exponential form is:

30762 = 2¹ × 3² × 1709¹

Step-3: Factors of 30744

List of positive integer factors of 30744 that divides 30744 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

Step-4: Factors of 30762

List of positive integer factors of 30762 that divides 30744 without a remainder.

1, 2, 3, 6, 9, 18, 1709, 3418, 5127, 10254, 15381

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30744 and 30762. The biggest common factor number is the GCF number.
So the greatest common factor 30744 and 30762 is 18.

Also check out the Least Common Multiple of 30744 and 30762