What is the Greatest Common Factor of 30744 and 30760?

Greatest common factor (GCF) of 30744 and 30760 is 8.

GCF(30744,30760) = 8

We will now calculate the prime factors of 30744 and 30760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30744 and 30760.

How to find the GCF of 30744 and 30760?

We will first find the prime factorization of 30744 and 30760. After we will calculate the factors of 30744 and 30760 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 30760

Prime factors of 30760 are 2, 5, 769. Prime factorization of 30760 in exponential form is:

30760 = 2³ × 5¹ × 769¹

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 30760

List of positive integer factors of 30760 that divides 30744 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 769, 1538, 3076, 3845, 6152, 7690, 15380

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30744 and 30760. The biggest common factor number is the GCF number.
So the greatest common factor 30744 and 30760 is 8.

Also check out the Least Common Multiple of 30744 and 30760