What is the Greatest Common Factor of 29805 and 29820?

Greatest common factor (GCF) of 29805 and 29820 is 15.

GCF(29805,29820) = 15

We will now calculate the prime factors of 29805 and 29820, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29805 and 29820.

How to find the GCF of 29805 and 29820?

We will first find the prime factorization of 29805 and 29820. After we will calculate the factors of 29805 and 29820 and find the biggest common factor number .

Step-1: Prime Factorization of 29805

Prime factors of 29805 are 3, 5, 1987. Prime factorization of 29805 in exponential form is:

29805 = 3¹ × 5¹ × 1987¹

Step-2: Prime Factorization of 29820

Prime factors of 29820 are 2, 3, 5, 7, 71. Prime factorization of 29820 in exponential form is:

29820 = 2² × 3¹ × 5¹ × 7¹ × 71¹

Step-3: Factors of 29805

List of positive integer factors of 29805 that divides 29805 without a remainder.

1, 3, 5, 15, 1987, 5961, 9935

Step-4: Factors of 29820

List of positive integer factors of 29820 that divides 29805 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 71, 84, 105, 140, 142, 210, 213, 284, 355, 420, 426, 497, 710, 852, 994, 1065, 1420, 1491, 1988, 2130, 2485, 2982, 4260, 4970, 5964, 7455, 9940, 14910

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29805 and 29820. The biggest common factor number is the GCF number.
So the greatest common factor 29805 and 29820 is 15.

Also check out the Least Common Multiple of 29805 and 29820