Greatest Common Factor of 34200 and 34208

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 34200, 34208 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 34200 and 34208 is 8.

GCF(34200,34208) = 8

GCF of 34200 and 34208

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

GCF of:
and

Greatest Common Factor of 34200 and 34208

GCF of 34200 and 34208 is 8

Prime Factorization of 34200


2 34200
2 17100
2 8550
3 4275
3 1425
5 475
5 95
19 19
1

Prime factors of 34200 are 2,3,5,19. Prime factorization of 34200 in exponential form is:

34200 = 23×32×52×191

Prime Factorization of 34208


2 34208
2 17104
2 8552
2 4276
2 2138
1069 1069
1

Prime factors of 34208 are 2,1069. Prime factorization of 34208 in exponential form is:

34208 = 25×10691

∴ So by taking common prime factors GCF of 34200 and 34208 is 8

Greatest Common Factor of 34200 and 34208 by matching factors method

Factors of 34200

List of positive integer factors of 34200 that divides 34200 without a remainder.

1,2,3,4,5,6,8,9,10,12,15,18,19,20,24,25,30,36,38,40,45,50,57,60,72,75,76,90,95,100,114,120,150,152,171,180,190,200,225,228,285,300,342,360,380,450,456,475,570,600,684,760,855,900,950,1140,1368,1425,1710,1800,1900,2280,2850,3420,3800,4275,5700,6840,8550,11400,17100,34200

Factors of 34208

List of positive integer factors of 34208 that divides 34208 without a remainder.

1,2,4,8,16,32,1069,2138,4276,8552,17104,34208

Greatest Common Factor

We found the factors and prime factorization of 34200 and 34208. The biggest common factor number is the GCF number.
So the greatest common factor 34200 and 34208 is 8.

Also check out the Least Common Multiple of 34200 and 34208

Properties of GCF 34200 and 34208

(i) The GCF of 34200 and 34208 is associative

GCF of 34200 and 34208 = GCF of 34208 and 34200

Related Greatest Common Factor of 34200

Related Greatest Common Factor of 34208

Frequently Asked Questions on GCF of 34200 and 34208

1. What is the GCF of 34200 and 34208?

Answer: GCF of 34200 and 34208 is 8.

2. What are the Factors of 34200?

Answer: Factors of 34200 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 25, 30, 36, 38, 40, 45, 50, 57, 60, 72, 75, 76, 90, 95, 100, 114, 120, 150, 152, 171, 180, 190, 200, 225, 228, 285, 300, 342, 360, 380, 450, 456, 475, 570, 600, 684, 760, 855, 900, 950, 1140, 1368, 1425, 1710, 1800, 1900, 2280, 2850, 3420, 3800, 4275, 5700, 6840, 8550, 11400, 17100, 34200. There are 72 integers that are factors of 34200. The greatest factor of 34200 is 34200.

3. What are the Factors of 34208?

Answer: Factors of 34208 are 1, 2, 4, 8, 16, 32, 1069, 2138, 4276, 8552, 17104, 34208. There are 12 integers that are factors of 34208. The greatest factor of 34208 is 34208.

4. How to Find the GCF of 34200 and 34208?

Answer:

Greatest Common Factor of 34200 and 34208 = 8

Step 1: Find the prime factorization of 34200

34200 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 19

Step 2: Find the prime factorization of 34208

34208 = 2 x 2 x 2 x 2 x 2 x 1069

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

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 34200 and 34208 is 8