Greatest Common Factor of 6 and 19

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

• Greatest Common Factor of 6 and 19 by prime factorization method
• Greatest Common Factor of 6 and 19 by matching factors method

Prime Factorization of 6

Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:

6 = 2¹×3¹

Prime Factorization of 19

Prime factors of 19 are 19. Prime factorization of 19 in exponential form is:

19 = 19¹

∴ So by taking common prime factors GCF of 6 and 19 is 1

Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1,2,3,6

Factors of 19

List of positive integer factors of 19 that divides 19 without a remainder.

1,19

Greatest Common Factor

We found the factors and prime factorization of 6 and 19. The biggest common factor number is the GCF number.
So the greatest common factor 6 and 19 is 1.

Also check out the Least Common Multiple of 6 and 19

(i) The GCF of 6 and 19 is associative

GCF of 6 and 19 = GCF of 19 and 6

1. What is the GCF of 6 and 19?

Answer: GCF of 6 and 19 is 1.

2. What are the Factors of 6?

Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.

3. What are the Factors of 19?

Answer: Factors of 19 are 1, 19. There are 2 integers that are factors of 19. The greatest factor of 19 is 19.

4. How to Find the GCF of 6 and 19?

Answer:

Greatest Common Factor of 6 and 19 = 1

Step 1: Find the prime factorization of 6

6 = 2 x 3

Step 2: Find the prime factorization of 19

19 = 19

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 6 and 19 is 1