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HCF of 726 and 275

HCF of 726 and 275 is the largest possible number that divides 726 and 275 exactly without any remainder. The factors of 726 and 275 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726 and 1, 5, 11, 25, 55, 275 respectively. There are 3 commonly used methods to find the HCF of 726 and 275 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 726 and 275
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 726 and 275?

Answer: HCF of 726 and 275 is 11.

Explanation:

The HCF of two non-zero integers, x(726) and y(275), is the highest positive integer m(11) that divides both x(726) and y(275) without any remainder.

Methods to Find HCF of 726 and 275

The methods to find the HCF of 726 and 275 are explained below.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

HCF of 726 and 275 by Long Division

HCF of 726 and 275 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 726 (larger number) by 275 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (275) by the remainder (176).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (11) is the HCF of 726 and 275.

HCF of 726 and 275 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 = 726 and Y = 275

HCF(726, 275) = HCF(275, 726 mod 275) = HCF(275, 176)
HCF(275, 176) = HCF(176, 275 mod 176) = HCF(176, 99)
HCF(176, 99) = HCF(99, 176 mod 99) = HCF(99, 77)
HCF(99, 77) = HCF(77, 99 mod 77) = HCF(77, 22)
HCF(77, 22) = HCF(22, 77 mod 22) = HCF(22, 11)
HCF(22, 11) = HCF(11, 22 mod 11) = HCF(11, 0)
HCF(11, 0) = 11 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 726 and 275 is 11.

HCF of 726 and 275 by Prime Factorization

Prime factorization of 726 and 275 is (2 × 3 × 11 × 11) and (5 × 5 × 11) respectively. As visible, 726 and 275 have only one common prime factor i.e. 11. Hence, the HCF of 726 and 275 is 11.

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HCF of 726 and 275 Examples

Example 1: For two numbers, HCF = 11 and LCM = 18150. If one number is 726, find the other number.

Solution:

Given: HCF (z, 726) = 11 and LCM (z, 726) = 18150
∵ HCF × LCM = 726 × (z)
⇒ z = (HCF × LCM)/726
⇒ z = (11 × 18150)/726
⇒ z = 275
Therefore, the other number is 275.
Example 2: Find the highest number that divides 726 and 275 exactly.

Solution:

The highest number that divides 726 and 275 exactly is their highest common factor, i.e. HCF of 726 and 275.
⇒ Factors of 726 and 275:
- Factors of 726 = 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726
- Factors of 275 = 1, 5, 11, 25, 55, 275
Therefore, the HCF of 726 and 275 is 11.
Example 3: Find the HCF of 726 and 275, if their LCM is 18150.

Solution:

∵ LCM × HCF = 726 × 275
⇒ HCF(726, 275) = (726 × 275)/18150 = 11
Therefore, the highest common factor of 726 and 275 is 11.

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FAQs on HCF of 726 and 275

What is the HCF of 726 and 275?

The HCF of 726 and 275 is 11. To calculate the Highest common factor of 726 and 275, we need to factor each number (factors of 726 = 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726; factors of 275 = 1, 5, 11, 25, 55, 275) and choose the highest factor that exactly divides both 726 and 275, i.e., 11.

How to Find the HCF of 726 and 275 by Long Division Method?

To find the HCF of 726, 275 using long division method, 726 is divided by 275. The corresponding divisor (11) when remainder equals 0 is taken as HCF.

If the HCF of 275 and 726 is 11, Find its LCM.

HCF(275, 726) × LCM(275, 726) = 275 × 726
Since the HCF of 275 and 726 = 11
⇒ 11 × LCM(275, 726) = 199650
Therefore, LCM = 18150
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 726 and 275?

There are three commonly used methods to find the HCF of 726 and 275.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the HCF of 726 and 275 by Prime Factorization?

To find the HCF of 726 and 275, we will find the prime factorization of the given numbers, i.e. 726 = 2 × 3 × 11 × 11; 275 = 5 × 5 × 11.
⇒ Since 11 is the only common prime factor of 726 and 275. Hence, HCF (726, 275) = 11.
☛ Prime Number

What is the Relation Between LCM and HCF of 726, 275?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 726 and 275, i.e. HCF × LCM = 726 × 275.

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