What is the Greatest Common Factor of 1102 and 1114?

Greatest common factor (GCF) of 1102 and 1114 is 2.

GCF(1102,1114) = 2

We will now calculate the prime factors of 1102 and 1114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1102 and 1114.

How to find the GCF of 1102 and 1114?

We will first find the prime factorization of 1102 and 1114. After we will calculate the factors of 1102 and 1114 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1114

Prime factors of 1114 are 2, 557. Prime factorization of 1114 in exponential form is:

1114 = 2¹ × 557¹

Step-3: Factors of 1102

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

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

Step-4: Factors of 1114

List of positive integer factors of 1114 that divides 1102 without a remainder.

1, 2, 557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1102 and 1114. The biggest common factor number is the GCF number.
So the greatest common factor 1102 and 1114 is 2.

Also check out the Least Common Multiple of 1102 and 1114