HCF of 34 and 102
HCF of 34 and 102 is the largest possible number that divides 34 and 102 exactly without any remainder. The factors of 34 and 102 are 1, 2, 17, 34 and 1, 2, 3, 6, 17, 34, 51, 102 respectively. There are 3 commonly used methods to find the HCF of 34 and 102 - long division, prime factorization, and Euclidean algorithm.
| 1. | HCF of 34 and 102 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 34 and 102?
Answer: HCF of 34 and 102 is 34.
Explanation:
The HCF of two non-zero integers, x(34) and y(102), is the highest positive integer m(34) that divides both x(34) and y(102) without any remainder.
Methods to Find HCF of 34 and 102
Let's look at the different methods for finding the HCF of 34 and 102.
- Listing Common Factors
- Prime Factorization Method
- Long Division Method
HCF of 34 and 102 by Listing Common Factors
- Factors of 34: 1, 2, 17, 34
- Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
There are 4 common factors of 34 and 102, that are 1, 2, 34, and 17. Therefore, the highest common factor of 34 and 102 is 34.
HCF of 34 and 102 by Prime Factorization
Prime factorization of 34 and 102 is (2 × 17) and (2 × 3 × 17) respectively. As visible, 34 and 102 have common prime factors. Hence, the HCF of 34 and 102 is 2 × 17 = 34.
HCF of 34 and 102 by Long Division
HCF of 34 and 102 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 102 (larger number) by 34 (smaller number).
- Step 2: Since the remainder = 0, the divisor (34) is the HCF of 34 and 102.
The corresponding divisor (34) is the HCF of 34 and 102.
☛ Also Check:
- HCF of 4 and 10 = 2
- HCF of 3 and 4 = 1
- HCF of 84 and 144 = 12
- HCF of 1 and 3 = 1
- HCF of 20, 25 and 30 = 5
- HCF of 72, 126 and 168 = 6
- HCF of 14 and 21 = 7
FAQs on HCF of 34 and 102
What is the HCF of 34 and 102?
The HCF of 34 and 102 is 34. To calculate the Highest common factor (HCF) of 34 and 102, we need to factor each number (factors of 34 = 1, 2, 17, 34; factors of 102 = 1, 2, 3, 6, 17, 34, 51, 102) and choose the highest factor that exactly divides both 34 and 102, i.e., 34.
If the HCF of 102 and 34 is 34, Find its LCM.
HCF(102, 34) × LCM(102, 34) = 102 × 34
Since the HCF of 102 and 34 = 34
⇒ 34 × LCM(102, 34) = 3468
Therefore, LCM = 102
☛ HCF Calculator
How to Find the HCF of 34 and 102 by Prime Factorization?
To find the HCF of 34 and 102, we will find the prime factorization of the given numbers, i.e. 34 = 2 × 17; 102 = 2 × 3 × 17.
⇒ Since 2, 17 are common terms in the prime factorization of 34 and 102. Hence, HCF(34, 102) = 2 × 17 = 34
☛ Prime Number
What are the Methods to Find HCF of 34 and 102?
There are three commonly used methods to find the HCF of 34 and 102.
- By Euclidean Algorithm
- By Long Division
- By Prime Factorization
How to Find the HCF of 34 and 102 by Long Division Method?
To find the HCF of 34, 102 using long division method, 102 is divided by 34. The corresponding divisor (34) when remainder equals 0 is taken as HCF.
What is the Relation Between LCM and HCF of 34, 102?
The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 34 and 102, i.e. HCF × LCM = 34 × 102.