Greatest Common Factor of 268 and 274

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 268, 274 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 268 and 274 is 2.

GCF(268,274) = 2

GCF of 268 and 274

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

GCF of:
and

Greatest Common Factor of 268 and 274

GCF of 268 and 274 is 2

Prime Factorization of 268


2 268
2 134
67 67
1

Prime factors of 268 are 2,67. Prime factorization of 268 in exponential form is:

268 = 22×671

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

∴ So by taking common prime factors GCF of 268 and 274 is 2

Greatest Common Factor of 268 and 274 by matching factors method

Factors of 268

List of positive integer factors of 268 that divides 268 without a remainder.

1,2,4,67,134,268

Factors of 274

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

1,2,137,274

Greatest Common Factor

We found the factors and prime factorization of 268 and 274. The biggest common factor number is the GCF number.
So the greatest common factor 268 and 274 is 2.

Also check out the Least Common Multiple of 268 and 274

Properties of GCF 268 and 274

(i) The GCF of 268 and 274 is associative

GCF of 268 and 274 = GCF of 274 and 268

Related Greatest Common Factor of 268

Related Greatest Common Factor of 274

Frequently Asked Questions on GCF of 268 and 274

1. What is the GCF of 268 and 274?

Answer: GCF of 268 and 274 is 2.

2. What are the Factors of 268?

Answer: Factors of 268 are 1, 2, 4, 67, 134, 268. There are 6 integers that are factors of 268. The greatest factor of 268 is 268.

3. 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.

4. How to Find the GCF of 268 and 274?

Answer:

Greatest Common Factor of 268 and 274 = 2

Step 1: Find the prime factorization of 268

268 = 2 x 2 x 67

Step 2: Find the prime factorization of 274

274 = 2 x 137

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 268 and 274 is 2