What is the Greatest Common Factor of 29940 and 29960?

Greatest common factor (GCF) of 29940 and 29960 is 20.

GCF(29940,29960) = 20

We will now calculate the prime factors of 29940 and 29960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29940 and 29960.

How to find the GCF of 29940 and 29960?

We will first find the prime factorization of 29940 and 29960. After we will calculate the factors of 29940 and 29960 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 29960

Prime factors of 29960 are 2, 5, 7, 107. Prime factorization of 29960 in exponential form is:

29960 = 2³ × 5¹ × 7¹ × 107¹

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 29960

List of positive integer factors of 29960 that divides 29940 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 107, 140, 214, 280, 428, 535, 749, 856, 1070, 1498, 2140, 2996, 3745, 4280, 5992, 7490, 14980

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29940 and 29960. The biggest common factor number is the GCF number.
So the greatest common factor 29940 and 29960 is 20.

Also check out the Least Common Multiple of 29940 and 29960