What is the Greatest Common Factor of 1084 and 1102?

Greatest common factor (GCF) of 1084 and 1102 is 2.

GCF(1084,1102) = 2

We will now calculate the prime factors of 1084 and 1102, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1084 and 1102.

How to find the GCF of 1084 and 1102?

We will first find the prime factorization of 1084 and 1102. After we will calculate the factors of 1084 and 1102 and find the biggest common factor number .

Step-1: Prime Factorization of 1084

Prime factors of 1084 are 2, 271. Prime factorization of 1084 in exponential form is:

1084 = 2² × 271¹

Step-2: Prime Factorization of 1102

Prime factors of 1102 are 2, 19, 29. Prime factorization of 1102 in exponential form is:

1102 = 2¹ × 19¹ × 29¹

Step-3: Factors of 1084

List of positive integer factors of 1084 that divides 1084 without a remainder.

1, 2, 4, 271, 542

Step-4: Factors of 1102

List of positive integer factors of 1102 that divides 1084 without a remainder.

1, 2, 19, 29, 38, 58, 551

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1084 and 1102. The biggest common factor number is the GCF number.
So the greatest common factor 1084 and 1102 is 2.

Also check out the Least Common Multiple of 1084 and 1102