What is the Greatest Common Factor of 105 and 109?

Greatest common factor (GCF) of 105 and 109 is 1.

GCF(105,109) = 1

We will now calculate the prime factors of 105 and 109, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 105 and 109.

How to find the GCF of 105 and 109?

We will first find the prime factorization of 105 and 109. After we will calculate the factors of 105 and 109 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 109

Prime factors of 109 are 109. Prime factorization of 109 in exponential form is:

109 = 109¹

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 109

List of positive integer factors of 109 that divides 105 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 105 and 109. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 109 is 1.

Also check out the Least Common Multiple of 105 and 109