Greatest Common Factor of 5200 and 5205

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 5200, 5205 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 5200 and 5205 is 5.

GCF(5200,5205) = 5

GCF of 5200 and 5205

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

GCF of:
and

Greatest Common Factor of 5200 and 5205

GCF of 5200 and 5205 is 5

Prime Factorization of 5200


2 5200
2 2600
2 1300
2 650
5 325
5 65
13 13
1

Prime factors of 5200 are 2,5,13. Prime factorization of 5200 in exponential form is:

5200 = 24×52×131

Prime Factorization of 5205


3 5205
5 1735
347 347
1

Prime factors of 5205 are 3,5,347. Prime factorization of 5205 in exponential form is:

5205 = 31×51×3471

∴ So by taking common prime factors GCF of 5200 and 5205 is 5

Greatest Common Factor of 5200 and 5205 by matching factors method

Factors of 5200

List of positive integer factors of 5200 that divides 5200 without a remainder.

1,2,4,5,8,10,13,16,20,25,26,40,50,52,65,80,100,104,130,200,208,260,325,400,520,650,1040,1300,2600,5200

Factors of 5205

List of positive integer factors of 5205 that divides 5205 without a remainder.

1,3,5,15,347,1041,1735,5205

Greatest Common Factor

We found the factors and prime factorization of 5200 and 5205. The biggest common factor number is the GCF number.
So the greatest common factor 5200 and 5205 is 5.

Also check out the Least Common Multiple of 5200 and 5205

Properties of GCF 5200 and 5205

(i) The GCF of 5200 and 5205 is associative

GCF of 5200 and 5205 = GCF of 5205 and 5200

Related Greatest Common Factor of 5200

Related Greatest Common Factor of 5205

Frequently Asked Questions on GCF of 5200 and 5205

1. What is the GCF of 5200 and 5205?

Answer: GCF of 5200 and 5205 is 5.

2. What are the Factors of 5200?

Answer: Factors of 5200 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 40, 50, 52, 65, 80, 100, 104, 130, 200, 208, 260, 325, 400, 520, 650, 1040, 1300, 2600, 5200. There are 30 integers that are factors of 5200. The greatest factor of 5200 is 5200.

3. What are the Factors of 5205?

Answer: Factors of 5205 are 1, 3, 5, 15, 347, 1041, 1735, 5205. There are 8 integers that are factors of 5205. The greatest factor of 5205 is 5205.

4. How to Find the GCF of 5200 and 5205?

Answer:

Greatest Common Factor of 5200 and 5205 = 5

Step 1: Find the prime factorization of 5200

5200 = 2 x 2 x 2 x 2 x 5 x 5 x 13

Step 2: Find the prime factorization of 5205

5205 = 3 x 5 x 347

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

GCF = 5

Step 4: Therefore, the greatest common factor of 5200 and 5205 is 5