What is the Greatest Common Factor of 1078 and 1092?

Greatest common factor (GCF) of 1078 and 1092 is 14.

GCF(1078,1092) = 14

We will now calculate the prime factors of 1078 and 1092, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1078 and 1092.

How to find the GCF of 1078 and 1092?

We will first find the prime factorization of 1078 and 1092. After we will calculate the factors of 1078 and 1092 and find the biggest common factor number .

Step-1: Prime Factorization of 1078

Prime factors of 1078 are 2, 7, 11. Prime factorization of 1078 in exponential form is:

1078 = 2¹ × 7² × 11¹

Step-2: Prime Factorization of 1092

Prime factors of 1092 are 2, 3, 7, 13. Prime factorization of 1092 in exponential form is:

1092 = 2² × 3¹ × 7¹ × 13¹

Step-3: Factors of 1078

List of positive integer factors of 1078 that divides 1078 without a remainder.

1, 2, 7, 11, 14, 22, 49, 77, 98, 154, 539

Step-4: Factors of 1092

List of positive integer factors of 1092 that divides 1078 without a remainder.

1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, 546

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1078 and 1092. The biggest common factor number is the GCF number.
So the greatest common factor 1078 and 1092 is 14.

Also check out the Least Common Multiple of 1078 and 1092