What is the Greatest Common Factor of 29925 and 29940?

Greatest common factor (GCF) of 29925 and 29940 is 15.

GCF(29925,29940) = 15

We will now calculate the prime factors of 29925 and 29940, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29925 and 29940.

How to find the GCF of 29925 and 29940?

We will first find the prime factorization of 29925 and 29940. After we will calculate the factors of 29925 and 29940 and find the biggest common factor number .

Step-1: Prime Factorization of 29925

Prime factors of 29925 are 3, 5, 7, 19. Prime factorization of 29925 in exponential form is:

29925 = 3² × 5² × 7¹ × 19¹

Step-2: 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-3: Factors of 29925

List of positive integer factors of 29925 that divides 29925 without a remainder.

1, 3, 5, 7, 9, 15, 19, 21, 25, 35, 45, 57, 63, 75, 95, 105, 133, 171, 175, 225, 285, 315, 399, 475, 525, 665, 855, 1197, 1425, 1575, 1995, 3325, 4275, 5985, 9975

Step-4: Factors of 29940

List of positive integer factors of 29940 that divides 29925 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29925 and 29940. The biggest common factor number is the GCF number.
So the greatest common factor 29925 and 29940 is 15.

Also check out the Least Common Multiple of 29925 and 29940