What is the Greatest Common Factor of 1085 and 1105?

Greatest common factor (GCF) of 1085 and 1105 is 5.

GCF(1085,1105) = 5

We will now calculate the prime factors of 1085 and 1105, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1085 and 1105.

How to find the GCF of 1085 and 1105?

We will first find the prime factorization of 1085 and 1105. After we will calculate the factors of 1085 and 1105 and find the biggest common factor number .

Step-1: Prime Factorization of 1085

Prime factors of 1085 are 5, 7, 31. Prime factorization of 1085 in exponential form is:

1085 = 5¹ × 7¹ × 31¹

Step-2: Prime Factorization of 1105

Prime factors of 1105 are 5, 13, 17. Prime factorization of 1105 in exponential form is:

1105 = 5¹ × 13¹ × 17¹

Step-3: Factors of 1085

List of positive integer factors of 1085 that divides 1085 without a remainder.

1, 5, 7, 31, 35, 155, 217

Step-4: Factors of 1105

List of positive integer factors of 1105 that divides 1085 without a remainder.

1, 5, 13, 17, 65, 85, 221

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1085 and 1105. The biggest common factor number is the GCF number.
So the greatest common factor 1085 and 1105 is 5.

Also check out the Least Common Multiple of 1085 and 1105