A day full of math games & activities. Find one near you.

GCF of 12 and 16

GCF of 12 and 16 is the largest possible number that divides 12 and 16 exactly without any remainder. The factors of 12 and 16 are 1, 2, 3, 4, 6, 12 and 1, 2, 4, 8, 16 respectively. There are 3 commonly used methods to find the GCF of 12 and 16 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 12 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 16?

Answer: GCF of 12 and 16 is 4.

Explanation:

The GCF of two non-zero integers, x(12) and y(16), is the greatest positive integer m(4) that divides both x(12) and y(16) without any remainder.

Methods to Find GCF of 12 and 16

Let's look at the different methods for finding the GCF of 12 and 16.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 12 and 16 by Long Division

GCF of 12 and 16 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 16 (larger number) by 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 12 and 16.

GCF of 12 and 16 by Prime Factorization

Prime factorization of 12 and 16 is (2 × 2 × 3) and (2 × 2 × 2 × 2) respectively. As visible, 12 and 16 have common prime factors. Hence, the GCF of 12 and 16 is 2 × 2 = 4.

GCF of 12 and 16 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 16: 1, 2, 4, 8, 16

There are 3 common factors of 12 and 16, that are 1, 2, and 4. Therefore, the greatest common factor of 12 and 16 is 4.

☛ Also Check:

GCF of 12 and 16 Examples

Example 1: The product of two numbers is 192. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 192
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 192/4
Therefore, the LCM is 48.
Example 2: Find the greatest number that divides 12 and 16 exactly.

Solution:

The greatest number that divides 12 and 16 exactly is their greatest common factor, i.e. GCF of 12 and 16.
⇒ Factors of 12 and 16:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 16 = 1, 2, 4, 8, 16
Therefore, the GCF of 12 and 16 is 4.
Example 3: Find the GCF of 12 and 16, if their LCM is 48.

Solution:

∵ LCM × GCF = 12 × 16
⇒ GCF(12, 16) = (12 × 16)/48 = 4
Therefore, the greatest common factor of 12 and 16 is 4.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 12 and 16

What is the GCF of 12 and 16?

The GCF of 12 and 16 is 4. To calculate the greatest common factor of 12 and 16, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 16 = 1, 2, 4, 8, 16) and choose the greatest factor that exactly divides both 12 and 16, i.e., 4.

What is the Relation Between LCM and GCF of 12, 16?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 12 and 16, i.e. GCF × LCM = 12 × 16.

If the GCF of 16 and 12 is 4, Find its LCM.

GCF(16, 12) × LCM(16, 12) = 16 × 12
Since the GCF of 16 and 12 = 4
⇒ 4 × LCM(16, 12) = 192
Therefore, LCM = 48
☛ GCF Calculator

How to Find the GCF of 12 and 16 by Prime Factorization?

To find the GCF of 12 and 16, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 16 = 2 × 2 × 2 × 2.
⇒ Since 2, 2 are common terms in the prime factorization of 12 and 16. Hence, GCF(12, 16) = 2 × 2 = 4
☛ Prime Number

How to Find the GCF of 12 and 16 by Long Division Method?

To find the GCF of 12, 16 using long division method, 16 is divided by 12. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 12 and 16?

There are three commonly used methods to find the GCF of 12 and 16.

By Listing Common Factors
By Long Division
By Prime Factorization

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum