HCF of 36 and 42
HCF of 36 and 42 is the largest possible number that divides 36 and 42 exactly without any remainder. The factors of 36 and 42 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the HCF of 36 and 42 - Euclidean algorithm, prime factorization, and long division.
| 1. | HCF of 36 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 36 and 42?
Answer: HCF of 36 and 42 is 6.
Explanation:
The HCF of two non-zero integers, x(36) and y(42), is the highest positive integer m(6) that divides both x(36) and y(42) without any remainder.
Methods to Find HCF of 36 and 42
Let's look at the different methods for finding the HCF of 36 and 42.
- Using Euclid's Algorithm
- Long Division Method
- Listing Common Factors
HCF of 36 and 42 by Euclidean Algorithm
As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 42 and Y = 36
- HCF(42, 36) = HCF(36, 42 mod 36) = HCF(36, 6)
- HCF(36, 6) = HCF(6, 36 mod 6) = HCF(6, 0)
- HCF(6, 0) = 6 (∵ HCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of HCF of 36 and 42 is 6.
HCF of 36 and 42 by Long Division
HCF of 36 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 36 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (6).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the HCF of 36 and 42.
HCF of 36 and 42 by Listing Common Factors
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 4 common factors of 36 and 42, that are 1, 2, 3, and 6. Therefore, the highest common factor of 36 and 42 is 6.
☛ Also Check:
- HCF of 144 and 180 = 36
- HCF of 3 and 5 = 1
- HCF of 84 and 144 = 12
- HCF of 36 and 84 = 12
- HCF of 391, 425 and 527 = 17
- HCF of 404 and 96 = 4
- HCF of 18 and 60 = 6
FAQs on HCF of 36 and 42
What is the HCF of 36 and 42?
The HCF of 36 and 42 is 6. To calculate the HCF (Highest Common Factor) of 36 and 42, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the highest factor that exactly divides both 36 and 42, i.e., 6.
How to Find the HCF of 36 and 42 by Long Division Method?
To find the HCF of 36, 42 using long division method, 42 is divided by 36. The corresponding divisor (6) when remainder equals 0 is taken as HCF.
How to Find the HCF of 36 and 42 by Prime Factorization?
To find the HCF of 36 and 42, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 42 = 2 × 3 × 7.
⇒ Since 2, 3 are common terms in the prime factorization of 36 and 42. Hence, HCF(36, 42) = 2 × 3 = 6
☛ Prime Number
What is the Relation Between LCM and HCF of 36, 42?
The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 36 and 42, i.e. HCF × LCM = 36 × 42.
What are the Methods to Find HCF of 36 and 42?
There are three commonly used methods to find the HCF of 36 and 42.
- By Long Division
- By Prime Factorization
- By Euclidean Algorithm
If the HCF of 42 and 36 is 6, Find its LCM.
HCF(42, 36) × LCM(42, 36) = 42 × 36
Since the HCF of 42 and 36 = 6
⇒ 6 × LCM(42, 36) = 1512
Therefore, LCM = 252
☛ Highest Common Factor Calculator