What is the Greatest Common Factor of 1530 and 1536?

Greatest common factor (GCF) of 1530 and 1536 is 6.

GCF(1530,1536) = 6

We will now calculate the prime factors of 1530 and 1536, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1530 and 1536.

How to find the GCF of 1530 and 1536?

We will first find the prime factorization of 1530 and 1536. After we will calculate the factors of 1530 and 1536 and find the biggest common factor number .

Step-1: Prime Factorization of 1530

Prime factors of 1530 are 2, 3, 5, 17. Prime factorization of 1530 in exponential form is:

1530 = 2¹ × 3² × 5¹ × 17¹

Step-2: Prime Factorization of 1536

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

1536 = 2⁹ × 3¹

Step-3: Factors of 1530

List of positive integer factors of 1530 that divides 1530 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 17, 18, 30, 34, 45, 51, 85, 90, 102, 153, 170, 255, 306, 510, 765

Step-4: Factors of 1536

List of positive integer factors of 1536 that divides 1530 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1530 and 1536. The biggest common factor number is the GCF number.
So the greatest common factor 1530 and 1536 is 6.

Also check out the Least Common Multiple of 1530 and 1536