Greatest Common Factor of 5200 and 5202

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, 5202 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 5200 and 5202 is 2.

GCF(5200,5202) = 2

GCF of 5200 and 5202

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

GCF of:
and

Greatest Common Factor of 5200 and 5202

GCF of 5200 and 5202 is 2

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 5202


2 5202
3 2601
3 867
17 289
17 17
1

Prime factors of 5202 are 2,3,17. Prime factorization of 5202 in exponential form is:

5202 = 21×32×172

∴ So by taking common prime factors GCF of 5200 and 5202 is 2

Greatest Common Factor of 5200 and 5202 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 5202

List of positive integer factors of 5202 that divides 5202 without a remainder.

1,2,3,6,9,17,18,34,51,102,153,289,306,578,867,1734,2601,5202

Greatest Common Factor

We found the factors and prime factorization of 5200 and 5202. The biggest common factor number is the GCF number.
So the greatest common factor 5200 and 5202 is 2.

Also check out the Least Common Multiple of 5200 and 5202

Properties of GCF 5200 and 5202

(i) The GCF of 5200 and 5202 is associative

GCF of 5200 and 5202 = GCF of 5202 and 5200

Related Greatest Common Factor of 5200

Related Greatest Common Factor of 5202

Frequently Asked Questions on GCF of 5200 and 5202

1. What is the GCF of 5200 and 5202?

Answer: GCF of 5200 and 5202 is 2.

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 5202?

Answer: Factors of 5202 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 289, 306, 578, 867, 1734, 2601, 5202. There are 18 integers that are factors of 5202. The greatest factor of 5202 is 5202.

4. How to Find the GCF of 5200 and 5202?

Answer:

Greatest Common Factor of 5200 and 5202 = 2

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 5202

5202 = 2 x 3 x 3 x 17 x 17

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

GCF = 2

Step 4: Therefore, the greatest common factor of 5200 and 5202 is 2