What is the Greatest Common Factor of 1138 and 1152?

Greatest common factor (GCF) of 1138 and 1152 is 2.

GCF(1138,1152) = 2

We will now calculate the prime factors of 1138 and 1152, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1138 and 1152.

How to find the GCF of 1138 and 1152?

We will first find the prime factorization of 1138 and 1152. After we will calculate the factors of 1138 and 1152 and find the biggest common factor number .

Step-1: Prime Factorization of 1138

Prime factors of 1138 are 2, 569. Prime factorization of 1138 in exponential form is:

1138 = 2¹ × 569¹

Step-2: Prime Factorization of 1152

Prime factors of 1152 are 2, 3. Prime factorization of 1152 in exponential form is:

1152 = 2⁷ × 3²

Step-3: Factors of 1138

List of positive integer factors of 1138 that divides 1138 without a remainder.

1, 2, 569

Step-4: Factors of 1152

List of positive integer factors of 1152 that divides 1138 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1138 and 1152. The biggest common factor number is the GCF number.
So the greatest common factor 1138 and 1152 is 2.

Also check out the Least Common Multiple of 1138 and 1152