What is the Greatest Common Factor of 105 and 114?

Greatest common factor (GCF) of 105 and 114 is 3.

GCF(105,114) = 3

We will now calculate the prime factors of 105 and 114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 105 and 114.

How to find the GCF of 105 and 114?

We will first find the prime factorization of 105 and 114. After we will calculate the factors of 105 and 114 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 114

Prime factors of 114 are 2, 3, 19. Prime factorization of 114 in exponential form is:

114 = 2¹ × 3¹ × 19¹

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 114

List of positive integer factors of 114 that divides 105 without a remainder.

1, 2, 3, 6, 19, 38, 57

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 105 and 114. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 114 is 3.

Also check out the Least Common Multiple of 105 and 114