Greatest Common Factor of 274 and 278

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 274, 278 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 274 and 278 is 2.

GCF(274,278) = 2

GCF of 274 and 278

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

GCF of:
and

Greatest Common Factor of 274 and 278

GCF of 274 and 278 is 2

Prime Factorization of 274


2 274
137 137
1

Prime factors of 274 are 2,137. Prime factorization of 274 in exponential form is:

274 = 21×1371

Prime Factorization of 278


2 278
139 139
1

Prime factors of 278 are 2,139. Prime factorization of 278 in exponential form is:

278 = 21×1391

∴ So by taking common prime factors GCF of 274 and 278 is 2

Greatest Common Factor of 274 and 278 by matching factors method

Factors of 274

List of positive integer factors of 274 that divides 274 without a remainder.

1,2,137,274

Factors of 278

List of positive integer factors of 278 that divides 278 without a remainder.

1,2,139,278

Greatest Common Factor

We found the factors and prime factorization of 274 and 278. The biggest common factor number is the GCF number.
So the greatest common factor 274 and 278 is 2.

Also check out the Least Common Multiple of 274 and 278

Properties of GCF 274 and 278

(i) The GCF of 274 and 278 is associative

GCF of 274 and 278 = GCF of 278 and 274

Related Greatest Common Factor of 274

Related Greatest Common Factor of 278

Frequently Asked Questions on GCF of 274 and 278

1. What is the GCF of 274 and 278?

Answer: GCF of 274 and 278 is 2.

2. What are the Factors of 274?

Answer: Factors of 274 are 1, 2, 137, 274. There are 4 integers that are factors of 274. The greatest factor of 274 is 274.

3. What are the Factors of 278?

Answer: Factors of 278 are 1, 2, 139, 278. There are 4 integers that are factors of 278. The greatest factor of 278 is 278.

4. How to Find the GCF of 274 and 278?

Answer:

Greatest Common Factor of 274 and 278 = 2

Step 1: Find the prime factorization of 274

274 = 2 x 137

Step 2: Find the prime factorization of 278

278 = 2 x 139

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 274 and 278 is 2