HCF of 18 and 42
HCF of 18 and 42 is the largest possible number that divides 18 and 42 exactly without any remainder. The factors of 18 and 42 are 1, 2, 3, 6, 9, 18 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the HCF of 18 and 42 - prime factorization, long division, and Euclidean algorithm.
| 1. | HCF of 18 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 18 and 42?
Answer: HCF of 18 and 42 is 6.
Explanation:
The HCF of two non-zero integers, x(18) and y(42), is the highest positive integer m(6) that divides both x(18) and y(42) without any remainder.
Methods to Find HCF of 18 and 42
Let's look at the different methods for finding the HCF of 18 and 42.
- Prime Factorization Method
- Listing Common Factors
- Long Division Method
HCF of 18 and 42 by Prime Factorization
Prime factorization of 18 and 42 is (2 × 3 × 3) and (2 × 3 × 7) respectively. As visible, 18 and 42 have common prime factors. Hence, the HCF of 18 and 42 is 2 × 3 = 6.
HCF of 18 and 42 by Listing Common Factors
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 4 common factors of 18 and 42, that are 1, 2, 3, and 6. Therefore, the highest common factor of 18 and 42 is 6.
HCF of 18 and 42 by Long Division
HCF of 18 and 42 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 42 (larger number) by 18 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (6).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the HCF of 18 and 42.
☛ Also Check:
- HCF of 28 and 36 = 4
- HCF of 3, 4 and 5 = 1
- HCF of 616 and 32 = 8
- HCF of 56, 96 and 404 = 4
- HCF of 144 and 192 = 48
- HCF of 0 and 6 = 6
- HCF of 56 and 88 = 8
FAQs on HCF of 18 and 42
What is the HCF of 18 and 42?
The HCF of 18 and 42 is 6. To calculate the HCF of 18 and 42, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the highest factor that exactly divides both 18 and 42, i.e., 6.
If the HCF of 42 and 18 is 6, Find its LCM.
HCF(42, 18) × LCM(42, 18) = 42 × 18
Since the HCF of 42 and 18 = 6
⇒ 6 × LCM(42, 18) = 756
Therefore, LCM = 126
☛ HCF Calculator
What is the Relation Between LCM and HCF of 18, 42?
The following equation can be used to express the relation between Least Common Multiple and HCF of 18 and 42, i.e. HCF × LCM = 18 × 42.
How to Find the HCF of 18 and 42 by Prime Factorization?
To find the HCF of 18 and 42, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 42 = 2 × 3 × 7.
⇒ Since 2, 3 are common terms in the prime factorization of 18 and 42. Hence, HCF(18, 42) = 2 × 3 = 6
☛ Prime Number
What are the Methods to Find HCF of 18 and 42?
There are three commonly used methods to find the HCF of 18 and 42.
- By Prime Factorization
- By Long Division
- By Euclidean Algorithm
How to Find the HCF of 18 and 42 by Long Division Method?
To find the HCF of 18, 42 using long division method, 42 is divided by 18. The corresponding divisor (6) when remainder equals 0 is taken as HCF.