What is the Greatest Common Factor of 29905 and 29925?

Greatest common factor (GCF) of 29905 and 29925 is 5.

GCF(29905,29925) = 5

We will now calculate the prime factors of 29905 and 29925, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29905 and 29925.

How to find the GCF of 29905 and 29925?

We will first find the prime factorization of 29905 and 29925. After we will calculate the factors of 29905 and 29925 and find the biggest common factor number .

Step-1: Prime Factorization of 29905

Prime factors of 29905 are 5, 5981. Prime factorization of 29905 in exponential form is:

29905 = 5¹ × 5981¹

Step-2: 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-3: Factors of 29905

List of positive integer factors of 29905 that divides 29905 without a remainder.

1, 5, 5981

Step-4: Factors of 29925

List of positive integer factors of 29925 that divides 29905 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29905 and 29925. The biggest common factor number is the GCF number.
So the greatest common factor 29905 and 29925 is 5.

Also check out the Least Common Multiple of 29905 and 29925