What is the Greatest Common Factor of 106 and 126?

Greatest common factor (GCF) of 106 and 126 is 2.

GCF(106,126) = 2

We will now calculate the prime factors of 106 and 126, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 106 and 126.

How to find the GCF of 106 and 126?

We will first find the prime factorization of 106 and 126. After we will calculate the factors of 106 and 126 and find the biggest common factor number .

Step-1: Prime Factorization of 106

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

106 = 2¹ × 53¹

Step-2: Prime Factorization of 126

Prime factors of 126 are 2, 3, 7. Prime factorization of 126 in exponential form is:

126 = 2¹ × 3² × 7¹

Step-3: Factors of 106

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

1, 2, 53

Step-4: Factors of 126

List of positive integer factors of 126 that divides 106 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 106 and 126. The biggest common factor number is the GCF number.
So the greatest common factor 106 and 126 is 2.

Also check out the Least Common Multiple of 106 and 126