Greatest Common Factor of 34194 and 34200

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 34194, 34200 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 34194 and 34200 is 6.

GCF(34194,34200) = 6

GCF of 34194 and 34200

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

GCF of:
and

Greatest Common Factor of 34194 and 34200

GCF of 34194 and 34200 is 6

Prime Factorization of 34194


2 34194
3 17097
41 5699
139 139
1

Prime factors of 34194 are 2,3,41,139. Prime factorization of 34194 in exponential form is:

34194 = 21×31×411×1391

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

∴ So by taking common prime factors GCF of 34194 and 34200 is 6

Greatest Common Factor of 34194 and 34200 by matching factors method

Factors of 34194

List of positive integer factors of 34194 that divides 34194 without a remainder.

1,2,3,6,41,82,123,139,246,278,417,834,5699,11398,17097,34194

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

Greatest Common Factor

We found the factors and prime factorization of 34194 and 34200. The biggest common factor number is the GCF number.
So the greatest common factor 34194 and 34200 is 6.

Also check out the Least Common Multiple of 34194 and 34200

Properties of GCF 34194 and 34200

(i) The GCF of 34194 and 34200 is associative

GCF of 34194 and 34200 = GCF of 34200 and 34194

Related Greatest Common Factor of 34194

Related Greatest Common Factor of 34200

Frequently Asked Questions on GCF of 34194 and 34200

1. What is the GCF of 34194 and 34200?

Answer: GCF of 34194 and 34200 is 6.

2. What are the Factors of 34194?

Answer: Factors of 34194 are 1, 2, 3, 6, 41, 82, 123, 139, 246, 278, 417, 834, 5699, 11398, 17097, 34194. There are 16 integers that are factors of 34194. The greatest factor of 34194 is 34194.

3. 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.

4. How to Find the GCF of 34194 and 34200?

Answer:

Greatest Common Factor of 34194 and 34200 = 6

Step 1: Find the prime factorization of 34194

34194 = 2 x 3 x 41 x 139

Step 2: Find the prime factorization of 34200

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

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 34194 and 34200 is 6