What is the Greatest Common Factor of 29820 and 29838?

Greatest common factor (GCF) of 29820 and 29838 is 6.

GCF(29820,29838) = 6

We will now calculate the prime factors of 29820 and 29838, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29820 and 29838.

How to find the GCF of 29820 and 29838?

We will first find the prime factorization of 29820 and 29838. After we will calculate the factors of 29820 and 29838 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 29838

Prime factors of 29838 are 2, 3, 4973. Prime factorization of 29838 in exponential form is:

29838 = 2¹ × 3¹ × 4973¹

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 29838

List of positive integer factors of 29838 that divides 29820 without a remainder.

1, 2, 3, 6, 4973, 9946, 14919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29820 and 29838. The biggest common factor number is the GCF number.
So the greatest common factor 29820 and 29838 is 6.

Also check out the Least Common Multiple of 29820 and 29838