What is the Greatest Common Factor of 770 and 784?

Greatest common factor (GCF) of 770 and 784 is 14.

GCF(770,784) = 14

We will now calculate the prime factors of 770 and 784, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 770 and 784.

How to find the GCF of 770 and 784?

We will first find the prime factorization of 770 and 784. After we will calculate the factors of 770 and 784 and find the biggest common factor number .

Step-1: Prime Factorization of 770

Prime factors of 770 are 2, 5, 7, 11. Prime factorization of 770 in exponential form is:

770 = 2¹ × 5¹ × 7¹ × 11¹

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 770

List of positive integer factors of 770 that divides 770 without a remainder.

1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385

Step-4: Factors of 784

List of positive integer factors of 784 that divides 770 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 770 and 784. The biggest common factor number is the GCF number.
So the greatest common factor 770 and 784 is 14.

Also check out the Least Common Multiple of 770 and 784