What is the Greatest Common Factor of 29940 and 29949?

Greatest common factor (GCF) of 29940 and 29949 is 3.

GCF(29940,29949) = 3

We will now calculate the prime factors of 29940 and 29949, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29940 and 29949.

How to find the GCF of 29940 and 29949?

We will first find the prime factorization of 29940 and 29949. After we will calculate the factors of 29940 and 29949 and find the biggest common factor number .

Step-1: Prime Factorization of 29940

Prime factors of 29940 are 2, 3, 5, 499. Prime factorization of 29940 in exponential form is:

29940 = 2² × 3¹ × 5¹ × 499¹

Step-2: Prime Factorization of 29949

Prime factors of 29949 are 3, 67, 149. Prime factorization of 29949 in exponential form is:

29949 = 3¹ × 67¹ × 149¹

Step-3: Factors of 29940

List of positive integer factors of 29940 that divides 29940 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 499, 998, 1497, 1996, 2495, 2994, 4990, 5988, 7485, 9980, 14970

Step-4: Factors of 29949

List of positive integer factors of 29949 that divides 29940 without a remainder.

1, 3, 67, 149, 201, 447, 9983

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29940 and 29949. The biggest common factor number is the GCF number.
So the greatest common factor 29940 and 29949 is 3.

Also check out the Least Common Multiple of 29940 and 29949