Greatest Common Factor of 2014 and 2017

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

• Greatest Common Factor of 2014 and 2017 by prime factorization method
• Greatest Common Factor of 2014 and 2017 by matching factors method

Prime Factorization of 2014

Prime factors of 2014 are 2,19,53. Prime factorization of 2014 in exponential form is:

2014 = 2¹×19¹×53¹

Prime Factorization of 2017

Prime factors of 2017 are 2017. Prime factorization of 2017 in exponential form is:

2017 = 2017¹

∴ So by taking common prime factors GCF of 2014 and 2017 is 1

Factors of 2014

List of positive integer factors of 2014 that divides 2014 without a remainder.

1,2,19,38,53,106,1007,2014

Factors of 2017

List of positive integer factors of 2017 that divides 2017 without a remainder.

1,2017

Greatest Common Factor

We found the factors and prime factorization of 2014 and 2017. The biggest common factor number is the GCF number.
So the greatest common factor 2014 and 2017 is 1.

Also check out the Least Common Multiple of 2014 and 2017

(i) The GCF of 2014 and 2017 is associative

GCF of 2014 and 2017 = GCF of 2017 and 2014

1. What is the GCF of 2014 and 2017?

Answer: GCF of 2014 and 2017 is 1.

2. What are the Factors of 2014?

Answer: Factors of 2014 are 1, 2, 19, 38, 53, 106, 1007, 2014. There are 8 integers that are factors of 2014. The greatest factor of 2014 is 2014.

3. What are the Factors of 2017?

Answer: Factors of 2017 are 1, 2017. There are 2 integers that are factors of 2017. The greatest factor of 2017 is 2017.

4. How to Find the GCF of 2014 and 2017?

Answer:

Greatest Common Factor of 2014 and 2017 = 1

Step 1: Find the prime factorization of 2014

2014 = 2 x 19 x 53

Step 2: Find the prime factorization of 2017

2017 = 2017

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 2014 and 2017 is 1