What is the Greatest Common Factor of 105 and 123?

Greatest common factor (GCF) of 105 and 123 is 3.

GCF(105,123) = 3

We will now calculate the prime factors of 105 and 123, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 105 and 123.

How to find the GCF of 105 and 123?

We will first find the prime factorization of 105 and 123. After we will calculate the factors of 105 and 123 and find the biggest common factor number .

Step-1: Prime Factorization of 105

Prime factors of 105 are 3, 5, 7. Prime factorization of 105 in exponential form is:

105 = 3¹ × 5¹ × 7¹

Step-2: Prime Factorization of 123

Prime factors of 123 are 3, 41. Prime factorization of 123 in exponential form is:

123 = 3¹ × 41¹

Step-3: Factors of 105

List of positive integer factors of 105 that divides 105 without a remainder.

1, 3, 5, 7, 15, 21, 35

Step-4: Factors of 123

List of positive integer factors of 123 that divides 105 without a remainder.

1, 3, 41

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 105 and 123. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 123 is 3.

Also check out the Least Common Multiple of 105 and 123