What is the Greatest Common Factor of 89 and 106?

Greatest common factor (GCF) of 89 and 106 is 1.

GCF(89,106) = 1

We will now calculate the prime factors of 89 and 106, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 89 and 106.

How to find the GCF of 89 and 106?

We will first find the prime factorization of 89 and 106. After we will calculate the factors of 89 and 106 and find the biggest common factor number .

Step-1: Prime Factorization of 89

Prime factors of 89 are 89. Prime factorization of 89 in exponential form is:

89 = 89¹

Step-2: Prime Factorization of 106

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

106 = 2¹ × 53¹

Step-3: Factors of 89

List of positive integer factors of 89 that divides 89 without a remainder.

Step-4: Factors of 106

List of positive integer factors of 106 that divides 89 without a remainder.

1, 2, 53

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 89 and 106. The biggest common factor number is the GCF number.
So the greatest common factor 89 and 106 is 1.

Also check out the Least Common Multiple of 89 and 106