What is the Greatest Common Factor of 24120 and 24138?

Greatest common factor (GCF) of 24120 and 24138 is 18.

GCF(24120,24138) = 18

We will now calculate the prime factors of 24120 and 24138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 24120 and 24138.

How to find the GCF of 24120 and 24138?

We will first find the prime factorization of 24120 and 24138. After we will calculate the factors of 24120 and 24138 and find the biggest common factor number .

Step-1: Prime Factorization of 24120

Prime factors of 24120 are 2, 3, 5, 67. Prime factorization of 24120 in exponential form is:

24120 = 2³ × 3² × 5¹ × 67¹

Step-2: Prime Factorization of 24138

Prime factors of 24138 are 2, 3, 149. Prime factorization of 24138 in exponential form is:

24138 = 2¹ × 3⁴ × 149¹

Step-3: Factors of 24120

List of positive integer factors of 24120 that divides 24120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 67, 72, 90, 120, 134, 180, 201, 268, 335, 360, 402, 536, 603, 670, 804, 1005, 1206, 1340, 1608, 2010, 2412, 2680, 3015, 4020, 4824, 6030, 8040, 12060

Step-4: Factors of 24138

List of positive integer factors of 24138 that divides 24120 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 149, 162, 298, 447, 894, 1341, 2682, 4023, 8046, 12069

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 24120 and 24138. The biggest common factor number is the GCF number.
So the greatest common factor 24120 and 24138 is 18.

Also check out the Least Common Multiple of 24120 and 24138