What is the Greatest Common Factor of 105 and 112?

Greatest common factor (GCF) of 105 and 112 is 7.

GCF(105,112) = 7

We will now calculate the prime factors of 105 and 112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 105 and 112.

How to find the GCF of 105 and 112?

We will first find the prime factorization of 105 and 112. After we will calculate the factors of 105 and 112 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 112

Prime factors of 112 are 2, 7. Prime factorization of 112 in exponential form is:

112 = 2⁴ × 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 112

List of positive integer factors of 112 that divides 105 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 105 and 112. The biggest common factor number is the GCF number.
So the greatest common factor 105 and 112 is 7.

Also check out the Least Common Multiple of 105 and 112