HCF of 455 and 42
HCF of 455 and 42 is the largest possible number that divides 455 and 42 exactly without any remainder. The factors of 455 and 42 are 1, 5, 7, 13, 35, 65, 91, 455 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the HCF of 455 and 42 - long division, prime factorization, and Euclidean algorithm.
| 1. | HCF of 455 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 455 and 42?
Answer: HCF of 455 and 42 is 7.
Explanation:
The HCF of two non-zero integers, x(455) and y(42), is the highest positive integer m(7) that divides both x(455) and y(42) without any remainder.
Methods to Find HCF of 455 and 42
Let's look at the different methods for finding the HCF of 455 and 42.
- Listing Common Factors
- Long Division Method
- Prime Factorization Method
HCF of 455 and 42 by Listing Common Factors
- Factors of 455: 1, 5, 7, 13, 35, 65, 91, 455
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 2 common factors of 455 and 42, that are 1 and 7. Therefore, the highest common factor of 455 and 42 is 7.
HCF of 455 and 42 by Long Division
HCF of 455 and 42 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 455 (larger number) by 42 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (35).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (7) is the HCF of 455 and 42.
HCF of 455 and 42 by Prime Factorization
Prime factorization of 455 and 42 is (5 × 7 × 13) and (2 × 3 × 7) respectively. As visible, 455 and 42 have only one common prime factor i.e. 7. Hence, the HCF of 455 and 42 is 7.
☛ Also Check:
- HCF of 40 and 80 = 40
- HCF of 12 and 36 = 12
- HCF of 391, 425 and 527 = 17
- HCF of 140 and 196 = 28
- HCF of 45 and 30 = 15
- HCF of 91, 112 and 49 = 7
- HCF of 9 and 12 = 3
FAQs on HCF of 455 and 42
What is the HCF of 455 and 42?
The HCF of 455 and 42 is 7. To calculate the Highest common factor (HCF) of 455 and 42, we need to factor each number (factors of 455 = 1, 5, 7, 13, 35, 65, 91, 455; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the highest factor that exactly divides both 455 and 42, i.e., 7.
If the HCF of 42 and 455 is 7, Find its LCM.
HCF(42, 455) × LCM(42, 455) = 42 × 455
Since the HCF of 42 and 455 = 7
⇒ 7 × LCM(42, 455) = 19110
Therefore, LCM = 2730
☛ Highest Common Factor Calculator
What are the Methods to Find HCF of 455 and 42?
There are three commonly used methods to find the HCF of 455 and 42.
- By Long Division
- By Prime Factorization
- By Listing Common Factors
What is the Relation Between LCM and HCF of 455, 42?
The following equation can be used to express the relation between Least Common Multiple and HCF of 455 and 42, i.e. HCF × LCM = 455 × 42.
How to Find the HCF of 455 and 42 by Prime Factorization?
To find the HCF of 455 and 42, we will find the prime factorization of the given numbers, i.e. 455 = 5 × 7 × 13; 42 = 2 × 3 × 7.
⇒ Since 7 is the only common prime factor of 455 and 42. Hence, HCF (455, 42) = 7.
☛ Prime Numbers
How to Find the HCF of 455 and 42 by Long Division Method?
To find the HCF of 455, 42 using long division method, 455 is divided by 42. The corresponding divisor (7) when remainder equals 0 is taken as HCF.