What is the Greatest Common Factor of 29820 and 29834?

Greatest common factor (GCF) of 29820 and 29834 is 14.

GCF(29820,29834) = 14

We will now calculate the prime factors of 29820 and 29834, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29820 and 29834.

How to find the GCF of 29820 and 29834?

We will first find the prime factorization of 29820 and 29834. After we will calculate the factors of 29820 and 29834 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 29834

Prime factors of 29834 are 2, 7, 2131. Prime factorization of 29834 in exponential form is:

29834 = 2¹ × 7¹ × 2131¹

Step-3: Factors of 29820

List of positive integer factors of 29820 that divides 29820 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

Step-4: Factors of 29834

List of positive integer factors of 29834 that divides 29820 without a remainder.

1, 2, 7, 14, 2131, 4262, 14917

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29820 and 29834. The biggest common factor number is the GCF number.
So the greatest common factor 29820 and 29834 is 14.

Also check out the Least Common Multiple of 29820 and 29834