What is the Greatest Common Factor of 105 and 168?

Greatest common factor (GCF) of 105 and 168 is 21.

GCF(105,168) = 21

We will now calculate the prime factors of 105 and 168, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 105 and 168.

How to find the GCF of 105 and 168?

We will first find the prime factorization of 105 and 168. After we will calculate the factors of 105 and 168 and find the biggest common factor number .

Step-1: Prime Factorization of 105

Prime factors of 105 are 3, 5, 7. Prime factorization of 105 in exponential form is:

105 = 3¹ × 5¹ × 7¹

Step-2: Prime Factorization of 168

Prime factors of 168 are 2, 3, 7. Prime factorization of 168 in exponential form is:

168 = 2³ × 3¹ × 7¹

Step-3: Factors of 105

List of positive integer factors of 105 that divides 105 without a remainder.

1, 3, 5, 7, 15, 21, 35

Step-4: Factors of 168

List of positive integer factors of 168 that divides 105 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 105 and 168. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 168 is 21.

Also check out the Least Common Multiple of 105 and 168