Greatest Common Factor of 1302 and 1309

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 1302, 1309 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1302 and 1309 is 7.

GCF(1302,1309) = 7

GCF of 1302 and 1309

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

GCF of:
and

Greatest Common Factor of 1302 and 1309

GCF of 1302 and 1309 is 7

Prime Factorization of 1302


2 1302
3 651
7 217
31 31
1

Prime factors of 1302 are 2,3,7,31. Prime factorization of 1302 in exponential form is:

1302 = 21×31×71×311

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

∴ So by taking common prime factors GCF of 1302 and 1309 is 7

Greatest Common Factor of 1302 and 1309 by matching factors method

Factors of 1302

List of positive integer factors of 1302 that divides 1302 without a remainder.

1,2,3,6,7,14,21,31,42,62,93,186,217,434,651,1302

Factors of 1309

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

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

Greatest Common Factor

We found the factors and prime factorization of 1302 and 1309. The biggest common factor number is the GCF number.
So the greatest common factor 1302 and 1309 is 7.

Also check out the Least Common Multiple of 1302 and 1309

Properties of GCF 1302 and 1309

(i) The GCF of 1302 and 1309 is associative

GCF of 1302 and 1309 = GCF of 1309 and 1302

Related Greatest Common Factor of 1302

Related Greatest Common Factor of 1309

Frequently Asked Questions on GCF of 1302 and 1309

1. What is the GCF of 1302 and 1309?

Answer: GCF of 1302 and 1309 is 7.

2. What are the Factors of 1302?

Answer: Factors of 1302 are 1, 2, 3, 6, 7, 14, 21, 31, 42, 62, 93, 186, 217, 434, 651, 1302. There are 16 integers that are factors of 1302. The greatest factor of 1302 is 1302.

3. 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.

4. How to Find the GCF of 1302 and 1309?

Answer:

Greatest Common Factor of 1302 and 1309 = 7

Step 1: Find the prime factorization of 1302

1302 = 2 x 3 x 7 x 31

Step 2: Find the prime factorization of 1309

1309 = 7 x 11 x 17

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

GCF = 7

Step 4: Therefore, the greatest common factor of 1302 and 1309 is 7