What is the Greatest Common Factor of 1106 and 1120?

Greatest common factor (GCF) of 1106 and 1120 is 14.

GCF(1106,1120) = 14

We will now calculate the prime factors of 1106 and 1120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1106 and 1120.

How to find the GCF of 1106 and 1120?

We will first find the prime factorization of 1106 and 1120. After we will calculate the factors of 1106 and 1120 and find the biggest common factor number .

Step-1: Prime Factorization of 1106

Prime factors of 1106 are 2, 7, 79. Prime factorization of 1106 in exponential form is:

1106 = 2¹ × 7¹ × 79¹

Step-2: Prime Factorization of 1120

Prime factors of 1120 are 2, 5, 7. Prime factorization of 1120 in exponential form is:

1120 = 2⁵ × 5¹ × 7¹

Step-3: Factors of 1106

List of positive integer factors of 1106 that divides 1106 without a remainder.

1, 2, 7, 14, 79, 158, 553

Step-4: Factors of 1120

List of positive integer factors of 1120 that divides 1106 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1106 and 1120. The biggest common factor number is the GCF number.
So the greatest common factor 1106 and 1120 is 14.

Also check out the Least Common Multiple of 1106 and 1120