Greatest Common Factor of 774 and 782

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 774, 782 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 774 and 782 is 2.

GCF(774,782) = 2

GCF of 774 and 782

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

GCF of:
and

Greatest Common Factor of 774 and 782

GCF of 774 and 782 is 2

Prime Factorization of 774


2 774
3 387
3 129
43 43
1

Prime factors of 774 are 2,3,43. Prime factorization of 774 in exponential form is:

774 = 21×32×431

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

∴ So by taking common prime factors GCF of 774 and 782 is 2

Greatest Common Factor of 774 and 782 by matching factors method

Factors of 774

List of positive integer factors of 774 that divides 774 without a remainder.

1,2,3,6,9,18,43,86,129,258,387,774

Factors of 782

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

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

Greatest Common Factor

We found the factors and prime factorization of 774 and 782. The biggest common factor number is the GCF number.
So the greatest common factor 774 and 782 is 2.

Also check out the Least Common Multiple of 774 and 782

Properties of GCF 774 and 782

(i) The GCF of 774 and 782 is associative

GCF of 774 and 782 = GCF of 782 and 774

Related Greatest Common Factor of 774

Related Greatest Common Factor of 782

Frequently Asked Questions on GCF of 774 and 782

1. What is the GCF of 774 and 782?

Answer: GCF of 774 and 782 is 2.

2. What are the Factors of 774?

Answer: Factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774. There are 12 integers that are factors of 774. The greatest factor of 774 is 774.

3. 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.

4. How to Find the GCF of 774 and 782?

Answer:

Greatest Common Factor of 774 and 782 = 2

Step 1: Find the prime factorization of 774

774 = 2 x 3 x 3 x 43

Step 2: Find the prime factorization of 782

782 = 2 x 17 x 23

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 774 and 782 is 2