Greatest Common Factor of 1296 and 1300

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 1296, 1300 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1296 and 1300 is 4.

GCF(1296,1300) = 4

GCF of 1296 and 1300

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

GCF of:
and

Greatest Common Factor of 1296 and 1300

GCF of 1296 and 1300 is 4

Prime Factorization of 1296


2 1296
2 648
2 324
2 162
3 81
3 27
3 9
3 3
1

Prime factors of 1296 are 2,3. Prime factorization of 1296 in exponential form is:

1296 = 24×34

Prime Factorization of 1300


2 1300
2 650
5 325
5 65
13 13
1

Prime factors of 1300 are 2,5,13. Prime factorization of 1300 in exponential form is:

1300 = 22×52×131

∴ So by taking common prime factors GCF of 1296 and 1300 is 4

Greatest Common Factor of 1296 and 1300 by matching factors method

Factors of 1296

List of positive integer factors of 1296 that divides 1296 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,81,108,144,162,216,324,432,648,1296

Factors of 1300

List of positive integer factors of 1300 that divides 1300 without a remainder.

1,2,4,5,10,13,20,25,26,50,52,65,100,130,260,325,650,1300

Greatest Common Factor

We found the factors and prime factorization of 1296 and 1300. The biggest common factor number is the GCF number.
So the greatest common factor 1296 and 1300 is 4.

Also check out the Least Common Multiple of 1296 and 1300

Properties of GCF 1296 and 1300

(i) The GCF of 1296 and 1300 is associative

GCF of 1296 and 1300 = GCF of 1300 and 1296

Related Greatest Common Factor of 1296

Related Greatest Common Factor of 1300

Frequently Asked Questions on GCF of 1296 and 1300

1. What is the GCF of 1296 and 1300?

Answer: GCF of 1296 and 1300 is 4.

2. What are the Factors of 1296?

Answer: Factors of 1296 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648, 1296. There are 25 integers that are factors of 1296. The greatest factor of 1296 is 1296.

3. What are the Factors of 1300?

Answer: Factors of 1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300. There are 18 integers that are factors of 1300. The greatest factor of 1300 is 1300.

4. How to Find the GCF of 1296 and 1300?

Answer:

Greatest Common Factor of 1296 and 1300 = 4

Step 1: Find the prime factorization of 1296

1296 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3

Step 2: Find the prime factorization of 1300

1300 = 2 x 2 x 5 x 5 x 13

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 1296 and 1300 is 4