Greatest Common Factor of 784 and 786

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 784, 786 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 784 and 786 is 2.

GCF(784,786) = 2

GCF of 784 and 786

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

GCF of:
and

Greatest Common Factor of 784 and 786

GCF of 784 and 786 is 2

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

Prime Factorization of 786


2 786
3 393
131 131
1

Prime factors of 786 are 2,3,131. Prime factorization of 786 in exponential form is:

786 = 21×31×1311

∴ So by taking common prime factors GCF of 784 and 786 is 2

Greatest Common Factor of 784 and 786 by matching factors method

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

Factors of 786

List of positive integer factors of 786 that divides 786 without a remainder.

1,2,3,6,131,262,393,786

Greatest Common Factor

We found the factors and prime factorization of 784 and 786. The biggest common factor number is the GCF number.
So the greatest common factor 784 and 786 is 2.

Also check out the Least Common Multiple of 784 and 786

Properties of GCF 784 and 786

(i) The GCF of 784 and 786 is associative

GCF of 784 and 786 = GCF of 786 and 784

Related Greatest Common Factor of 784

Related Greatest Common Factor of 786

Frequently Asked Questions on GCF of 784 and 786

1. What is the GCF of 784 and 786?

Answer: GCF of 784 and 786 is 2.

2. 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.

3. What are the Factors of 786?

Answer: Factors of 786 are 1, 2, 3, 6, 131, 262, 393, 786. There are 8 integers that are factors of 786. The greatest factor of 786 is 786.

4. How to Find the GCF of 784 and 786?

Answer:

Greatest Common Factor of 784 and 786 = 2

Step 1: Find the prime factorization of 784

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

Step 2: Find the prime factorization of 786

786 = 2 x 3 x 131

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

GCF = 2

Step 4: Therefore, the greatest common factor of 784 and 786 is 2