Greatest Common Factor of 109 and 111

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

• Greatest Common Factor of 109 and 111 by prime factorization method
• Greatest Common Factor of 109 and 111 by matching factors method

Prime Factorization of 109

Prime factors of 109 are 109. Prime factorization of 109 in exponential form is:

109 = 109¹

Prime Factorization of 111

Prime factors of 111 are 3.Prime factorization of 111 in exponential form is:

111 = 3¹×37¹

∴ So by taking common prime factors GCF of 109 and 111 is 1

Factors of 109

List of positive integer factors of 109 that divides 109 without a remainder.

1,109

Factors of 111

List of positive integer factors of 111 that divides 111 without a remainder.

1,3,37,111

Greatest Common Factor

We found the factors and prime factorization of 109 and 111. The biggest common factor number is the GCF number.
So the greatest common factor 109 and 111 is 1.

Also check out the Least Common Multiple of 109 and 111

(i) The GCF of 109 and 111 is associative

GCF of 109 and 111 = GCF of 111 and 109

1. What is the GCF of 109 and 111?

Answer: GCF of 109 and 111 is 1.

2. What are the Factors of 109?

Answer: Factors of 109 are 1, 109. There are 2 integers that are factors of 109. The greatest factor of 109 is 109.

3. What are the Factors of 111?

Answer: Factors of 111 are 1, 3, 37, 111. There are 4 integers that are factors of 111. The greatest factor of 111 is 111.

4. How to Find the GCF of 109 and 111?

Answer:

Greatest Common Factor of 109 and 111 = 1

Step 1: Find the prime factorization of 109

109 = 109

Step 2: Find the prime factorization of 111

111 = 3 x 37

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 109 and 111 is 1