What is the Greatest Common Factor of 1536 and 1540?

Greatest common factor (GCF) of 1536 and 1540 is 4.

GCF(1536,1540) = 4

We will now calculate the prime factors of 1536 and 1540, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1536 and 1540.

How to find the GCF of 1536 and 1540?

We will first find the prime factorization of 1536 and 1540. After we will calculate the factors of 1536 and 1540 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 1540

Prime factors of 1540 are 2, 5, 7, 11. Prime factorization of 1540 in exponential form is:

1540 = 2² × 5¹ × 7¹ × 11¹

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 1540

List of positive integer factors of 1540 that divides 1536 without a remainder.

1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1536 and 1540. The biggest common factor number is the GCF number.
So the greatest common factor 1536 and 1540 is 4.

Also check out the Least Common Multiple of 1536 and 1540