HCF of 126 and 156
HCF of 126 and 156 is the largest possible number that divides 126 and 156 exactly without any remainder. The factors of 126 and 156 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 and 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156 respectively. There are 3 commonly used methods to find the HCF of 126 and 156 - Euclidean algorithm, prime factorization, and long division.
| 1. | HCF of 126 and 156 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 126 and 156?
Answer: HCF of 126 and 156 is 6.
Explanation:
The HCF of two non-zero integers, x(126) and y(156), is the highest positive integer m(6) that divides both x(126) and y(156) without any remainder.
Methods to Find HCF of 126 and 156
Let's look at the different methods for finding the HCF of 126 and 156.
- Prime Factorization Method
- Long Division Method
- Using Euclid's Algorithm
HCF of 126 and 156 by Prime Factorization
Prime factorization of 126 and 156 is (2 × 3 × 3 × 7) and (2 × 2 × 3 × 13) respectively. As visible, 126 and 156 have common prime factors. Hence, the HCF of 126 and 156 is 2 × 3 = 6.
HCF of 126 and 156 by Long Division
HCF of 126 and 156 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 156 (larger number) by 126 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (126) by the remainder (30).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the HCF of 126 and 156.
HCF of 126 and 156 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 = 156 and Y = 126
- HCF(156, 126) = HCF(126, 156 mod 126) = HCF(126, 30)
- HCF(126, 30) = HCF(30, 126 mod 30) = HCF(30, 6)
- HCF(30, 6) = HCF(6, 30 mod 6) = HCF(6, 0)
- HCF(6, 0) = 6 (∵ HCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of HCF of 126 and 156 is 6.
☛ Also Check:
- HCF of 32 and 56 = 8
- HCF of 12 and 14 = 2
- HCF of 96 and 404 = 4
- HCF of 6 and 8 = 2
- HCF of 84 and 144 = 12
- HCF of 2 and 4 = 2
- HCF of 15, 25 and 30 = 5
FAQs on HCF of 126 and 156
What is the HCF of 126 and 156?
The HCF of 126 and 156 is 6. To calculate the HCF (Highest Common Factor) of 126 and 156, we need to factor each number (factors of 126 = 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126; factors of 156 = 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156) and choose the highest factor that exactly divides both 126 and 156, i.e., 6.
How to Find the HCF of 126 and 156 by Long Division Method?
To find the HCF of 126, 156 using long division method, 156 is divided by 126. The corresponding divisor (6) when remainder equals 0 is taken as HCF.
How to Find the HCF of 126 and 156 by Prime Factorization?
To find the HCF of 126 and 156, we will find the prime factorization of the given numbers, i.e. 126 = 2 × 3 × 3 × 7; 156 = 2 × 2 × 3 × 13.
⇒ Since 2, 3 are common terms in the prime factorization of 126 and 156. Hence, HCF(126, 156) = 2 × 3 = 6
☛ What is a Prime Number?
If the HCF of 156 and 126 is 6, Find its LCM.
HCF(156, 126) × LCM(156, 126) = 156 × 126
Since the HCF of 156 and 126 = 6
⇒ 6 × LCM(156, 126) = 19656
Therefore, LCM = 3276
☛ HCF Calculator
What are the Methods to Find HCF of 126 and 156?
There are three commonly used methods to find the HCF of 126 and 156.
- By Long Division
- By Euclidean Algorithm
- By Prime Factorization
What is the Relation Between LCM and HCF of 126, 156?
The following equation can be used to express the relation between LCM and HCF of 126 and 156, i.e. HCF × LCM = 126 × 156.