Greatest Common Factor of 106 and 111

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

• Greatest Common Factor of 106 and 111 by prime factorization method
• Greatest Common Factor of 106 and 111 by matching factors method

Prime Factorization of 106

Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:

106 = 2¹×53¹

Prime Factorization of 111

Prime factors of 111 are 3,37. Prime factorization of 111 in exponential form is:

111 = 3¹×37¹

∴ So by taking common prime factors GCF of 106 and 111 is 1

Factors of 106

List of positive integer factors of 106 that divides 106 without a remainder.

1,2,53,106

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 106 and 111. The biggest common factor number is the GCF number.
So the greatest common factor 106 and 111 is 1.

Also check out the Least Common Multiple of 106 and 111

(i) The GCF of 106 and 111 is associative

GCF of 106 and 111 = GCF of 111 and 106

1. What is the GCF of 106 and 111?

Answer: GCF of 106 and 111 is 1.

2. What are the Factors of 106?

Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.

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 106 and 111?

Answer:

Greatest Common Factor of 106 and 111 = 1

Step 1: Find the prime factorization of 106

106 = 2 x 53

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 106 and 111 is 1