HCF of 72 and 126
HCF of 72 and 126 is the largest possible number that divides 72 and 126 exactly without any remainder. The factors of 72 and 126 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 respectively. There are 3 commonly used methods to find the HCF of 72 and 126 - long division, Euclidean algorithm, and prime factorization.
| 1. | HCF of 72 and 126 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is HCF of 72 and 126?
Answer: HCF of 72 and 126 is 18.
Explanation:
The HCF of two non-zero integers, x(72) and y(126), is the highest positive integer m(18) that divides both x(72) and y(126) without any remainder.
Methods to Find HCF of 72 and 126
The methods to find the HCF of 72 and 126 are explained below.
- Long Division Method
- Using Euclid's Algorithm
- Listing Common Factors
HCF of 72 and 126 by Long Division
HCF of 72 and 126 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 126 (larger number) by 72 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (72) by the remainder (54).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (18) is the HCF of 72 and 126.
HCF of 72 and 126 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 = 126 and Y = 72
- HCF(126, 72) = HCF(72, 126 mod 72) = HCF(72, 54)
- HCF(72, 54) = HCF(54, 72 mod 54) = HCF(54, 18)
- HCF(54, 18) = HCF(18, 54 mod 18) = HCF(18, 0)
- HCF(18, 0) = 18 (∵ HCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of HCF of 72 and 126 is 18.
HCF of 72 and 126 by Listing Common Factors
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
There are 6 common factors of 72 and 126, that are 1, 2, 3, 6, 9, and 18. Therefore, the highest common factor of 72 and 126 is 18.
☛ Also Check:
- HCF of 81 and 237 = 3
- HCF of 56 and 84 = 28
- HCF of 336, 240 and 96 = 48
- HCF of 2923 and 3239 = 79
- HCF of 26 and 91 = 13
- HCF of 85 and 153 = 17
- HCF of 255 and 867 = 51
FAQs on HCF of 72 and 126
What is the HCF of 72 and 126?
The HCF of 72 and 126 is 18. To calculate the Highest common factor (HCF) of 72 and 126, we need to factor each number (factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; factors of 126 = 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126) and choose the highest factor that exactly divides both 72 and 126, i.e., 18.
What is the Relation Between LCM and HCF of 72, 126?
The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 72 and 126, i.e. HCF × LCM = 72 × 126.
How to Find the HCF of 72 and 126 by Long Division Method?
To find the HCF of 72, 126 using long division method, 126 is divided by 72. The corresponding divisor (18) when remainder equals 0 is taken as HCF.
What are the Methods to Find HCF of 72 and 126?
There are three commonly used methods to find the HCF of 72 and 126.
- By Long Division
- By Prime Factorization
- By Listing Common Factors
If the HCF of 126 and 72 is 18, Find its LCM.
HCF(126, 72) × LCM(126, 72) = 126 × 72
Since the HCF of 126 and 72 = 18
⇒ 18 × LCM(126, 72) = 9072
Therefore, LCM = 504
☛ HCF Calculator
How to Find the HCF of 72 and 126 by Prime Factorization?
To find the HCF of 72 and 126, we will find the prime factorization of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 126 = 2 × 3 × 3 × 7.
⇒ Since 2, 3, 3 are common terms in the prime factorization of 72 and 126. Hence, HCF(72, 126) = 2 × 3 × 3 = 18
☛ Prime Numbers