What is the Greatest Common Factor of 1085 and 1100?

Greatest common factor (GCF) of 1085 and 1100 is 5.

GCF(1085,1100) = 5

We will now calculate the prime factors of 1085 and 1100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1085 and 1100.

How to find the GCF of 1085 and 1100?

We will first find the prime factorization of 1085 and 1100. After we will calculate the factors of 1085 and 1100 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 1100

Prime factors of 1100 are 2, 5, 11. Prime factorization of 1100 in exponential form is:

1100 = 2² × 5² × 11¹

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 1100

List of positive integer factors of 1100 that divides 1085 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1085 and 1100. The biggest common factor number is the GCF number.
So the greatest common factor 1085 and 1100 is 5.

Also check out the Least Common Multiple of 1085 and 1100