What is the Greatest Common Factor of 105 and 110?

Greatest common factor (GCF) of 105 and 110 is 5.

GCF(105,110) = 5

We will now calculate the prime factors of 105 and 110, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 105 and 110.

How to find the GCF of 105 and 110?

We will first find the prime factorization of 105 and 110. After we will calculate the factors of 105 and 110 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 110

Prime factors of 110 are 2, 5, 11. Prime factorization of 110 in exponential form is:

110 = 2¹ × 5¹ × 11¹

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 110

List of positive integer factors of 110 that divides 105 without a remainder.

1, 2, 5, 10, 11, 22, 55

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 105 and 110. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 110 is 5.

Also check out the Least Common Multiple of 105 and 110