What is the Greatest Common Factor of 1054 and 1065?

Greatest common factor (GCF) of 1054 and 1065 is 1.

GCF(1054,1065) = 1

We will now calculate the prime factors of 1054 and 1065, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1054 and 1065.

How to find the GCF of 1054 and 1065?

We will first find the prime factorization of 1054 and 1065. After we will calculate the factors of 1054 and 1065 and find the biggest common factor number .

Step-1: Prime Factorization of 1054

Prime factors of 1054 are 2, 17, 31. Prime factorization of 1054 in exponential form is:

1054 = 2¹ × 17¹ × 31¹

Step-2: Prime Factorization of 1065

Prime factors of 1065 are 3, 5, 71. Prime factorization of 1065 in exponential form is:

1065 = 3¹ × 5¹ × 71¹

Step-3: Factors of 1054

List of positive integer factors of 1054 that divides 1054 without a remainder.

1, 2, 17, 31, 34, 62, 527

Step-4: Factors of 1065

List of positive integer factors of 1065 that divides 1054 without a remainder.

1, 3, 5, 15, 71, 213, 355

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1054 and 1065. The biggest common factor number is the GCF number.
So the greatest common factor 1054 and 1065 is 1.

Also check out the Least Common Multiple of 1054 and 1065