Greatest Common Factor of 782 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 782, 784 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 782 and 784 is 2.

GCF(782,784) = 2

GCF of 782 and 784

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

GCF of:
and

Greatest Common Factor of 782 and 784

GCF of 782 and 784 is 2

Prime Factorization of 782


2 782
17 391
23 23
1

Prime factors of 782 are 2,17,23. Prime factorization of 782 in exponential form is:

782 = 21×171×231

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 782 and 784 is 2

Greatest Common Factor of 782 and 784 by matching factors method

Factors of 782

List of positive integer factors of 782 that divides 782 without a remainder.

1,2,17,23,34,46,391,782

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 782 and 784. The biggest common factor number is the GCF number.
So the greatest common factor 782 and 784 is 2.

Also check out the Least Common Multiple of 782 and 784

Properties of GCF 782 and 784

(i) The GCF of 782 and 784 is associative

GCF of 782 and 784 = GCF of 784 and 782

Related Greatest Common Factor of 782

Related Greatest Common Factor of 784

Frequently Asked Questions on GCF of 782 and 784

1. What is the GCF of 782 and 784?

Answer: GCF of 782 and 784 is 2.

2. What are the Factors of 782?

Answer: Factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782. There are 8 integers that are factors of 782. The greatest factor of 782 is 782.

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 782 and 784?

Answer:

Greatest Common Factor of 782 and 784 = 2

Step 1: Find the prime factorization of 782

782 = 2 x 17 x 23

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 = 2

Step 4: Therefore, the greatest common factor of 782 and 784 is 2