GCF of 18 and 40
GCF of 18 and 40 is the largest possible number that divides 18 and 40 exactly without any remainder. The factors of 18 and 40 are 1, 2, 3, 6, 9, 18 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 commonly used methods to find the GCF of 18 and 40 - Euclidean algorithm, long division, and prime factorization.
| 1. | GCF of 18 and 40 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 18 and 40?
Answer: GCF of 18 and 40 is 2.
Explanation:
The GCF of two non-zero integers, x(18) and y(40), is the greatest positive integer m(2) that divides both x(18) and y(40) without any remainder.
Methods to Find GCF of 18 and 40
Let's look at the different methods for finding the GCF of 18 and 40.
- Prime Factorization Method
- Listing Common Factors
- Long Division Method
GCF of 18 and 40 by Prime Factorization
Prime factorization of 18 and 40 is (2 × 3 × 3) and (2 × 2 × 2 × 5) respectively. As visible, 18 and 40 have only one common prime factor i.e. 2. Hence, the GCF of 18 and 40 is 2.
GCF of 18 and 40 by Listing Common Factors
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
There are 2 common factors of 18 and 40, that are 1 and 2. Therefore, the greatest common factor of 18 and 40 is 2.
GCF of 18 and 40 by Long Division
GCF of 18 and 40 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 40 (larger number) by 18 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (4).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (2) is the GCF of 18 and 40.
☛ Also Check:
- GCF of 48 and 64 = 16
- GCF of 68 and 102 = 34
- GCF of 21 and 24 = 3
- GCF of 15 and 40 = 5
- GCF of 16 and 72 = 8
- GCF of 42 and 90 = 6
- GCF of 38 and 57 = 19
FAQs on GCF of 18 and 40
What is the GCF of 18 and 40?
The GCF of 18 and 40 is 2. To calculate the greatest common factor of 18 and 40, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the greatest factor that exactly divides both 18 and 40, i.e., 2.
What is the Relation Between LCM and GCF of 18, 40?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 18 and 40, i.e. GCF × LCM = 18 × 40.
How to Find the GCF of 18 and 40 by Long Division Method?
To find the GCF of 18, 40 using long division method, 40 is divided by 18. The corresponding divisor (2) when remainder equals 0 is taken as GCF.
How to Find the GCF of 18 and 40 by Prime Factorization?
To find the GCF of 18 and 40, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 40 = 2 × 2 × 2 × 5.
⇒ Since 2 is the only common prime factor of 18 and 40. Hence, GCF (18, 40) = 2.
☛ Prime Numbers
What are the Methods to Find GCF of 18 and 40?
There are three commonly used methods to find the GCF of 18 and 40.
- By Prime Factorization
- By Euclidean Algorithm
- By Long Division
If the GCF of 40 and 18 is 2, Find its LCM.
GCF(40, 18) × LCM(40, 18) = 40 × 18
Since the GCF of 40 and 18 = 2
⇒ 2 × LCM(40, 18) = 720
Therefore, LCM = 360
☛ Greatest Common Factor Calculator