What is the Greatest Common Factor of 30724 and 30740?

Greatest common factor (GCF) of 30724 and 30740 is 4.

GCF(30724,30740) = 4

We will now calculate the prime factors of 30724 and 30740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30724 and 30740.

How to find the GCF of 30724 and 30740?

We will first find the prime factorization of 30724 and 30740. After we will calculate the factors of 30724 and 30740 and find the biggest common factor number .

Step-1: Prime Factorization of 30724

Prime factors of 30724 are 2, 7681. Prime factorization of 30724 in exponential form is:

30724 = 2² × 7681¹

Step-2: Prime Factorization of 30740

Prime factors of 30740 are 2, 5, 29, 53. Prime factorization of 30740 in exponential form is:

30740 = 2² × 5¹ × 29¹ × 53¹

Step-3: Factors of 30724

List of positive integer factors of 30724 that divides 30724 without a remainder.

1, 2, 4, 7681, 15362

Step-4: Factors of 30740

List of positive integer factors of 30740 that divides 30724 without a remainder.

1, 2, 4, 5, 10, 20, 29, 53, 58, 106, 116, 145, 212, 265, 290, 530, 580, 1060, 1537, 3074, 6148, 7685, 15370

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30724 and 30740. The biggest common factor number is the GCF number.
So the greatest common factor 30724 and 30740 is 4.

Also check out the Least Common Multiple of 30724 and 30740