Greatest Common Factor of 1309 and 1314

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 1309, 1314 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1309 and 1314 is 1.

GCF(1309,1314) = 1

GCF of 1309 and 1314

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

GCF of:
and

Greatest Common Factor of 1309 and 1314

GCF of 1309 and 1314 is 1

Prime Factorization of 1309


7 1309
11 187
17 17
1

Prime factors of 1309 are 7,11,17. Prime factorization of 1309 in exponential form is:

1309 = 71×111×171

Prime Factorization of 1314


2 1314
3 657
3 219
73 73
1

Prime factors of 1314 are 2,3,73. Prime factorization of 1314 in exponential form is:

1314 = 21×32×731

∴ So by taking common prime factors GCF of 1309 and 1314 is 1

Greatest Common Factor of 1309 and 1314 by matching factors method

Factors of 1309

List of positive integer factors of 1309 that divides 1309 without a remainder.

1,7,11,17,77,119,187,1309

Factors of 1314

List of positive integer factors of 1314 that divides 1314 without a remainder.

1,2,3,6,9,18,73,146,219,438,657,1314

Greatest Common Factor

We found the factors and prime factorization of 1309 and 1314. The biggest common factor number is the GCF number.
So the greatest common factor 1309 and 1314 is 1.

Also check out the Least Common Multiple of 1309 and 1314

Properties of GCF 1309 and 1314

(i) The GCF of 1309 and 1314 is associative

GCF of 1309 and 1314 = GCF of 1314 and 1309

Related Greatest Common Factor of 1309

Related Greatest Common Factor of 1314

Frequently Asked Questions on GCF of 1309 and 1314

1. What is the GCF of 1309 and 1314?

Answer: GCF of 1309 and 1314 is 1.

2. What are the Factors of 1309?

Answer: Factors of 1309 are 1, 7, 11, 17, 77, 119, 187, 1309. There are 8 integers that are factors of 1309. The greatest factor of 1309 is 1309.

3. What are the Factors of 1314?

Answer: Factors of 1314 are 1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657, 1314. There are 12 integers that are factors of 1314. The greatest factor of 1314 is 1314.

4. How to Find the GCF of 1309 and 1314?

Answer:

Greatest Common Factor of 1309 and 1314 = 1

Step 1: Find the prime factorization of 1309

1309 = 7 x 11 x 17

Step 2: Find the prime factorization of 1314

1314 = 2 x 3 x 3 x 73

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 1309 and 1314 is 1