GCF of 18 and 32 is the largest possible number that divides 18 and 32 exactly without any remainder. The factors of 18 and 32 are 1, 2, 3, 6, 9, 18 and 1, 2, 4, 8, 16, 32 respectively. There are 3 commonly used methods to find the GCF of 18 and 32 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 18 and 32 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 18 and 32?
Answer: GCF of 18 and 32 is 2.
Explanation:
The GCF of two non-zero integers, x(18) and y(32), is the greatest positive integer m(2) that divides both x(18) and y(32) without any remainder.
Methods to Find GCF of 18 and 32
Let's look at the different methods for finding the GCF of 18 and 32.
- Listing Common Factors
- Long Division Method
- Prime Factorization Method
GCF of 18 and 32 by Listing Common Factors
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 32: 1, 2, 4, 8, 16, 32
There are 2 common factors of 18 and 32, that are 1 and 2. Therefore, the greatest common factor of 18 and 32 is 2.
GCF of 18 and 32 by Long Division
GCF of 18 and 32 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 32 (larger number) by 18 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (14).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (2) is the GCF of 18 and 32.
GCF of 18 and 32 by Prime Factorization
Prime factorization of 18 and 32 is (2 × 3 × 3) and (2 × 2 × 2 × 2 × 2) respectively. As visible, 18 and 32 have only one common prime factor i.e. 2. Hence, the GCF of 18 and 32 is 2.
☛ Also Check:
- GCF of 7 and 21 = 7
- GCF of 21 and 28 = 7
- GCF of 18 and 24 = 6
- GCF of 60 and 70 = 10
- GCF of 4 and 15 = 1
- GCF of 64 and 96 = 32
- GCF of 28 and 63 = 7
GCF of 18 and 32 Examples
Example 1: Find the GCF of 18 and 32, if their LCM is 288.
Solution:
∵ LCM × GCF = 18 × 32
⇒ GCF(18, 32) = (18 × 32)/288 = 2
Therefore, the greatest common factor of 18 and 32 is 2.Example 2: For two numbers, GCF = 2 and LCM = 288. If one number is 18, find the other number.
Solution:
Given: GCF (z, 18) = 2 and LCM (z, 18) = 288
∵ GCF × LCM = 18 × (z)
⇒ z = (GCF × LCM)/18
⇒ z = (2 × 288)/18
⇒ z = 32
Therefore, the other number is 32.Example 3: The product of two numbers is 576. If their GCF is 2, what is their LCM?
Solution:
Given: GCF = 2 and product of numbers = 576
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 576/2
Therefore, the LCM is 288.
Show Solution >
go to slidego to slidego 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 18 and 32
What is the GCF of 18 and 32?
The GCF of 18 and 32 is 2. To calculate the GCF of 18 and 32, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 32 = 1, 2, 4, 8, 16, 32) and choose the greatest factor that exactly divides both 18 and 32, i.e., 2.
How to Find the GCF of 18 and 32 by Long Division Method?
To find the GCF of 18, 32 using long division method, 32 is divided by 18. The corresponding divisor (2) when remainder equals 0 is taken as GCF.
What is the Relation Between LCM and GCF of 18, 32?
The following equation can be used to express the relation between Least Common Multiple and GCF of 18 and 32, i.e. GCF × LCM = 18 × 32.
How to Find the GCF of 18 and 32 by Prime Factorization?
To find the GCF of 18 and 32, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 32 = 2 × 2 × 2 × 2 × 2.
⇒ Since 2 is the only common prime factor of 18 and 32. Hence, GCF (18, 32) = 2.
☛ What is a Prime Number?
What are the Methods to Find GCF of 18 and 32?
There are three commonly used methods to find the GCF of 18 and 32.
- By Prime Factorization
- By Long Division
- By Listing Common Factors
If the GCF of 32 and 18 is 2, Find its LCM.
GCF(32, 18) × LCM(32, 18) = 32 × 18
Since the GCF of 32 and 18 = 2
⇒ 2 × LCM(32, 18) = 576
Therefore, LCM = 288
☛ GCF Calculator
