What is the Greatest Common Factor of 768 and 784?

Greatest common factor (GCF) of 768 and 784 is 16.

GCF(768,784) = 16

We will now calculate the prime factors of 768 and 784, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 768 and 784.

How to find the GCF of 768 and 784?

We will first find the prime factorization of 768 and 784. After we will calculate the factors of 768 and 784 and find the biggest common factor number .

Step-1: Prime Factorization of 768

Prime factors of 768 are 2, 3. Prime factorization of 768 in exponential form is:

768 = 2⁸ × 3¹

Step-2: Prime Factorization of 784

Prime factors of 784 are 2, 7. Prime factorization of 784 in exponential form is:

784 = 2⁴ × 7²

Step-3: Factors of 768

List of positive integer factors of 768 that divides 768 without a remainder.

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

Step-4: Factors of 784

List of positive integer factors of 784 that divides 768 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 768 and 784. The biggest common factor number is the GCF number.
So the greatest common factor 768 and 784 is 16.

Also check out the Least Common Multiple of 768 and 784