Greatest Common Factor of 1302 and 1305

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, 1305 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1302 and 1305 is 3.

GCF(1302,1305) = 3

GCF of 1302 and 1305

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

GCF of:
and

Greatest Common Factor of 1302 and 1305

GCF of 1302 and 1305 is 3

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 1305


3 1305
3 435
5 145
29 29
1

Prime factors of 1305 are 3,5,29. Prime factorization of 1305 in exponential form is:

1305 = 32×51×291

∴ So by taking common prime factors GCF of 1302 and 1305 is 3

Greatest Common Factor of 1302 and 1305 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 1305

List of positive integer factors of 1305 that divides 1305 without a remainder.

1,3,5,9,15,29,45,87,145,261,435,1305

Greatest Common Factor

We found the factors and prime factorization of 1302 and 1305. The biggest common factor number is the GCF number.
So the greatest common factor 1302 and 1305 is 3.

Also check out the Least Common Multiple of 1302 and 1305

Properties of GCF 1302 and 1305

(i) The GCF of 1302 and 1305 is associative

GCF of 1302 and 1305 = GCF of 1305 and 1302

Related Greatest Common Factor of 1302

Related Greatest Common Factor of 1305

Frequently Asked Questions on GCF of 1302 and 1305

1. What is the GCF of 1302 and 1305?

Answer: GCF of 1302 and 1305 is 3.

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 1305?

Answer: Factors of 1305 are 1, 3, 5, 9, 15, 29, 45, 87, 145, 261, 435, 1305. There are 12 integers that are factors of 1305. The greatest factor of 1305 is 1305.

4. How to Find the GCF of 1302 and 1305?

Answer:

Greatest Common Factor of 1302 and 1305 = 3

Step 1: Find the prime factorization of 1302

1302 = 2 x 3 x 7 x 31

Step 2: Find the prime factorization of 1305

1305 = 3 x 3 x 5 x 29

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

GCF = 3

Step 4: Therefore, the greatest common factor of 1302 and 1305 is 3