Greatest Common Factor of 10 and 19

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

• Greatest Common Factor of 10 and 19 by prime factorization method
• Greatest Common Factor of 10 and 19 by matching factors method

Prime Factorization of 10

Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:

10 = 2¹×5¹

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 10 and 19 is 1

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1,2,5,10

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 10 and 19. The biggest common factor number is the GCF number.
So the greatest common factor 10 and 19 is 1.

Also check out the Least Common Multiple of 10 and 19

(i) The GCF of 10 and 19 is associative

GCF of 10 and 19 = GCF of 19 and 10

1. What is the GCF of 10 and 19?

Answer: GCF of 10 and 19 is 1.

2. What are the Factors of 10?

Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.

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 10 and 19?

Answer:

Greatest Common Factor of 10 and 19 = 1

Step 1: Find the prime factorization of 10

10 = 2 x 5

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 10 and 19 is 1