Greatest Common Factor of 101 and 106

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

• Greatest Common Factor of 101 and 106 by prime factorization method
• Greatest Common Factor of 101 and 106 by matching factors method

Prime Factorization of 101

Prime factors of 101 are 101. Prime factorization of 101 in exponential form is:

101 = 101¹

Prime Factorization of 106

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

106 = 2¹×53¹

∴ So by taking common prime factors GCF of 101 and 106 is 1

Factors of 101

List of positive integer factors of 101 that divides 101 without a remainder.

1,101

Factors of 106

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

1,2,53,106

Greatest Common Factor

We found the factors and prime factorization of 101 and 106. The biggest common factor number is the GCF number.
So the greatest common factor 101 and 106 is 1.

Also check out the Least Common Multiple of 101 and 106

(i) The GCF of 101 and 106 is associative

GCF of 101 and 106 = GCF of 106 and 101

1. What is the GCF of 101 and 106?

Answer: GCF of 101 and 106 is 1.

2. What are the Factors of 101?

Answer: Factors of 101 are 1, 101. There are 2 integers that are factors of 101. The greatest factor of 101 is 101.

3. 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.

4. How to Find the GCF of 101 and 106?

Answer:

Greatest Common Factor of 101 and 106 = 1

Step 1: Find the prime factorization of 101

101 = 101

Step 2: Find the prime factorization of 106

106 = 2 x 53

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 101 and 106 is 1