What is the Greatest Common Factor of 1536 and 1545?

Greatest common factor (GCF) of 1536 and 1545 is 3.

GCF(1536,1545) = 3

We will now calculate the prime factors of 1536 and 1545, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1536 and 1545.

How to find the GCF of 1536 and 1545?

We will first find the prime factorization of 1536 and 1545. After we will calculate the factors of 1536 and 1545 and find the biggest common factor number .

Step-1: Prime Factorization of 1536

Prime factors of 1536 are 2, 3. Prime factorization of 1536 in exponential form is:

1536 = 2⁹ × 3¹

Step-2: Prime Factorization of 1545

Prime factors of 1545 are 3, 5, 103. Prime factorization of 1545 in exponential form is:

1545 = 3¹ × 5¹ × 103¹

Step-3: Factors of 1536

List of positive integer factors of 1536 that divides 1536 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768

Step-4: Factors of 1545

List of positive integer factors of 1545 that divides 1536 without a remainder.

1, 3, 5, 15, 103, 309, 515

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1536 and 1545. The biggest common factor number is the GCF number.
So the greatest common factor 1536 and 1545 is 3.

Also check out the Least Common Multiple of 1536 and 1545