Greatest Common Factor of 777 and 784

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 777, 784 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 777 and 784 is 7.

GCF(777,784) = 7

GCF of 777 and 784

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 777 and 784

GCF of 777 and 784 is 7

Prime Factorization of 777


3 777
7 259
37 37
1

Prime factors of 777 are 3,7,37. Prime factorization of 777 in exponential form is:

777 = 31×71×371

Prime Factorization of 784


2 784
2 392
2 196
2 98
7 49
7 7
1

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

784 = 24×72

∴ So by taking common prime factors GCF of 777 and 784 is 7

Greatest Common Factor of 777 and 784 by matching factors method

Factors of 777

List of positive integer factors of 777 that divides 777 without a remainder.

1,3,7,21,37,111,259,777

Factors of 784

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

1,2,4,7,8,14,16,28,49,56,98,112,196,392,784

Greatest Common Factor

We found the factors and prime factorization of 777 and 784. The biggest common factor number is the GCF number.
So the greatest common factor 777 and 784 is 7.

Also check out the Least Common Multiple of 777 and 784

Properties of GCF 777 and 784

(i) The GCF of 777 and 784 is associative

GCF of 777 and 784 = GCF of 784 and 777

Related Greatest Common Factor of 777

Related Greatest Common Factor of 784

Frequently Asked Questions on GCF of 777 and 784

1. What is the GCF of 777 and 784?

Answer: GCF of 777 and 784 is 7.

2. What are the Factors of 777?

Answer: Factors of 777 are 1, 3, 7, 21, 37, 111, 259, 777. There are 8 integers that are factors of 777. The greatest factor of 777 is 777.

3. What are the Factors of 784?

Answer: Factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784. There are 15 integers that are factors of 784. The greatest factor of 784 is 784.

4. How to Find the GCF of 777 and 784?

Answer:

Greatest Common Factor of 777 and 784 = 7

Step 1: Find the prime factorization of 777

777 = 3 x 7 x 37

Step 2: Find the prime factorization of 784

784 = 2 x 2 x 2 x 2 x 7 x 7

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 7

Step 4: Therefore, the greatest common factor of 777 and 784 is 7