HCF of 105 and 154
HCF of 105 and 154 is the largest possible number that divides 105 and 154 exactly without any remainder. The factors of 105 and 154 are 1, 3, 5, 7, 15, 21, 35, 105 and 1, 2, 7, 11, 14, 22, 77, 154 respectively. There are 3 commonly used methods to find the HCF of 105 and 154 - prime factorization, long division, and Euclidean algorithm.
| 1. | HCF of 105 and 154 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 105 and 154?
Answer: HCF of 105 and 154 is 7.
Explanation:
The HCF of two non-zero integers, x(105) and y(154), is the highest positive integer m(7) that divides both x(105) and y(154) without any remainder.
Methods to Find HCF of 105 and 154
Let's look at the different methods for finding the HCF of 105 and 154.
- Long Division Method
- Listing Common Factors
- Prime Factorization Method
HCF of 105 and 154 by Long Division
HCF of 105 and 154 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 154 (larger number) by 105 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (105) by the remainder (49).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (7) is the HCF of 105 and 154.
HCF of 105 and 154 by Listing Common Factors
- Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
- Factors of 154: 1, 2, 7, 11, 14, 22, 77, 154
There are 2 common factors of 105 and 154, that are 1 and 7. Therefore, the highest common factor of 105 and 154 is 7.
HCF of 105 and 154 by Prime Factorization
Prime factorization of 105 and 154 is (3 × 5 × 7) and (2 × 7 × 11) respectively. As visible, 105 and 154 have only one common prime factor i.e. 7. Hence, the HCF of 105 and 154 is 7.
☛ Also Check:
- HCF of 20 and 35 = 5
- HCF of 4 and 5 = 1
- HCF of 12, 18 and 24 = 6
- HCF of 28 and 36 = 4
- HCF of 186 and 403 = 31
- HCF of 8, 10 and 12 = 2
- HCF of 120, 144 and 204 = 12
FAQs on HCF of 105 and 154
What is the HCF of 105 and 154?
The HCF of 105 and 154 is 7. To calculate the HCF (Highest Common Factor) of 105 and 154, we need to factor each number (factors of 105 = 1, 3, 5, 7, 15, 21, 35, 105; factors of 154 = 1, 2, 7, 11, 14, 22, 77, 154) and choose the highest factor that exactly divides both 105 and 154, i.e., 7.
How to Find the HCF of 105 and 154 by Long Division Method?
To find the HCF of 105, 154 using long division method, 154 is divided by 105. The corresponding divisor (7) when remainder equals 0 is taken as HCF.
What is the Relation Between LCM and HCF of 105, 154?
The following equation can be used to express the relation between Least Common Multiple and HCF of 105 and 154, i.e. HCF × LCM = 105 × 154.
If the HCF of 154 and 105 is 7, Find its LCM.
HCF(154, 105) × LCM(154, 105) = 154 × 105
Since the HCF of 154 and 105 = 7
⇒ 7 × LCM(154, 105) = 16170
Therefore, LCM = 2310
☛ Highest Common Factor Calculator
How to Find the HCF of 105 and 154 by Prime Factorization?
To find the HCF of 105 and 154, we will find the prime factorization of the given numbers, i.e. 105 = 3 × 5 × 7; 154 = 2 × 7 × 11.
⇒ Since 7 is the only common prime factor of 105 and 154. Hence, HCF (105, 154) = 7.
☛ Prime Number
What are the Methods to Find HCF of 105 and 154?
There are three commonly used methods to find the HCF of 105 and 154.
- By Listing Common Factors
- By Long Division
- By Prime Factorization