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

GCF of 16 and 24

GCF of 16 and 24 is the largest possible number that divides 16 and 24 exactly without any remainder. The factors of 16 and 24 are 1, 2, 4, 8, 16 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are 3 commonly used methods to find the GCF of 16 and 24 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 16 and 24
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 24?

Answer: GCF of 16 and 24 is 8.

Explanation:

The GCF of two non-zero integers, x(16) and y(24), is the greatest positive integer m(8) that divides both x(16) and y(24) without any remainder.

Methods to Find GCF of 16 and 24

The methods to find the GCF of 16 and 24 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 16 and 24 by Long Division

GCF of 16 and 24 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 24 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the GCF of 16 and 24.

GCF of 16 and 24 by Prime Factorization

Prime factorization of 16 and 24 is (2 × 2 × 2 × 2) and (2 × 2 × 2 × 3) respectively. As visible, 16 and 24 have common prime factors. Hence, the GCF of 16 and 24 is 2 × 2 × 2 = 8.

GCF of 16 and 24 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

There are 4 common factors of 16 and 24, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 16 and 24 is 8.

☛ Also Check:

GCF of 16 and 24 Examples

Example 1: For two numbers, GCF = 8 and LCM = 48. If one number is 24, find the other number.

Solution:

Given: GCF (z, 24) = 8 and LCM (z, 24) = 48
∵ GCF × LCM = 24 × (z)
⇒ z = (GCF × LCM)/24
⇒ z = (8 × 48)/24
⇒ z = 16
Therefore, the other number is 16.
Example 2: Find the GCF of 16 and 24, if their LCM is 48.

Solution:

∵ LCM × GCF = 16 × 24
⇒ GCF(16, 24) = (16 × 24)/48 = 8
Therefore, the greatest common factor of 16 and 24 is 8.
Example 3: Find the greatest number that divides 16 and 24 exactly.

Solution:

The greatest number that divides 16 and 24 exactly is their greatest common factor, i.e. GCF of 16 and 24.
⇒ Factors of 16 and 24:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Therefore, the GCF of 16 and 24 is 8.

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 16 and 24

What is the GCF of 16 and 24?

The GCF of 16 and 24 is 8. To calculate the GCF (Greatest Common Factor) of 16 and 24, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the greatest factor that exactly divides both 16 and 24, i.e., 8.

What are the Methods to Find GCF of 16 and 24?

There are three commonly used methods to find the GCF of 16 and 24.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 16 and 24 by Prime Factorization?

To find the GCF of 16 and 24, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 24 = 2 × 2 × 2 × 3.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 16 and 24. Hence, GCF(16, 24) = 2 × 2 × 2 = 8
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 16, 24?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 16 and 24, i.e. GCF × LCM = 16 × 24.

If the GCF of 24 and 16 is 8, Find its LCM.

GCF(24, 16) × LCM(24, 16) = 24 × 16
Since the GCF of 24 and 16 = 8
⇒ 8 × LCM(24, 16) = 384
Therefore, LCM = 48
☛ GCF Calculator

How to Find the GCF of 16 and 24 by Long Division Method?

To find the GCF of 16, 24 using long division method, 24 is divided by 16. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum