What is the Greatest Common Factor of 29806 and 29820?

Greatest common factor (GCF) of 29806 and 29820 is 14.

GCF(29806,29820) = 14

We will now calculate the prime factors of 29806 and 29820, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29806 and 29820.

How to find the GCF of 29806 and 29820?

We will first find the prime factorization of 29806 and 29820. After we will calculate the factors of 29806 and 29820 and find the biggest common factor number .

Step-1: Prime Factorization of 29806

Prime factors of 29806 are 2, 7, 2129. Prime factorization of 29806 in exponential form is:

29806 = 2¹ × 7¹ × 2129¹

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 29806

List of positive integer factors of 29806 that divides 29806 without a remainder.

1, 2, 7, 14, 2129, 4258, 14903

Step-4: Factors of 29820

List of positive integer factors of 29820 that divides 29806 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 29806 and 29820. The biggest common factor number is the GCF number.
So the greatest common factor 29806 and 29820 is 14.

Also check out the Least Common Multiple of 29806 and 29820