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HCF of 272 and 425

HCF of 272 and 425 is the largest possible number that divides 272 and 425 exactly without any remainder. The factors of 272 and 425 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272 and 1, 5, 17, 25, 85, 425 respectively. There are 3 commonly used methods to find the HCF of 272 and 425 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 272 and 425
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 272 and 425?

Answer: HCF of 272 and 425 is 17.

Explanation:

The HCF of two non-zero integers, x(272) and y(425), is the highest positive integer m(17) that divides both x(272) and y(425) without any remainder.

Methods to Find HCF of 272 and 425

The methods to find the HCF of 272 and 425 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

HCF of 272 and 425 by Prime Factorization

Prime factorization of 272 and 425 is (2 × 2 × 2 × 2 × 17) and (5 × 5 × 17) respectively. As visible, 272 and 425 have only one common prime factor i.e. 17. Hence, the HCF of 272 and 425 is 17.

HCF of 272 and 425 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 = 425 and Y = 272

HCF(425, 272) = HCF(272, 425 mod 272) = HCF(272, 153)
HCF(272, 153) = HCF(153, 272 mod 153) = HCF(153, 119)
HCF(153, 119) = HCF(119, 153 mod 119) = HCF(119, 34)
HCF(119, 34) = HCF(34, 119 mod 34) = HCF(34, 17)
HCF(34, 17) = HCF(17, 34 mod 17) = HCF(17, 0)
HCF(17, 0) = 17 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 272 and 425 is 17.

HCF of 272 and 425 by Long Division

HCF of 272 and 425 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 425 (larger number) by 272 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (272) by the remainder (153).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (17) is the HCF of 272 and 425.

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HCF of 272 and 425 Examples

Example 1: Find the highest number that divides 272 and 425 exactly.

Solution:

The highest number that divides 272 and 425 exactly is their highest common factor, i.e. HCF of 272 and 425.
⇒ Factors of 272 and 425:
- Factors of 272 = 1, 2, 4, 8, 16, 17, 34, 68, 136, 272
- Factors of 425 = 1, 5, 17, 25, 85, 425
Therefore, the HCF of 272 and 425 is 17.
Example 2: The product of two numbers is 115600. If their HCF is 17, what is their LCM?

Solution:

Given: HCF = 17 and product of numbers = 115600
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 115600/17
Therefore, the LCM is 6800.
Example 3: For two numbers, HCF = 17 and LCM = 6800. If one number is 272, find the other number.

Solution:

Given: HCF (y, 272) = 17 and LCM (y, 272) = 6800
∵ HCF × LCM = 272 × (y)
⇒ y = (HCF × LCM)/272
⇒ y = (17 × 6800)/272
⇒ y = 425
Therefore, the other number is 425.

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FAQs on HCF of 272 and 425

What is the HCF of 272 and 425?

The HCF of 272 and 425 is 17. To calculate the Highest common factor (HCF) of 272 and 425, we need to factor each number (factors of 272 = 1, 2, 4, 8, 16, 17, 34, 68, 136, 272; factors of 425 = 1, 5, 17, 25, 85, 425) and choose the highest factor that exactly divides both 272 and 425, i.e., 17.

How to Find the HCF of 272 and 425 by Prime Factorization?

To find the HCF of 272 and 425, we will find the prime factorization of the given numbers, i.e. 272 = 2 × 2 × 2 × 2 × 17; 425 = 5 × 5 × 17.
⇒ Since 17 is the only common prime factor of 272 and 425. Hence, HCF (272, 425) = 17.
☛ Prime Number

What is the Relation Between LCM and HCF of 272, 425?

The following equation can be used to express the relation between LCM and HCF of 272 and 425, i.e. HCF × LCM = 272 × 425.

How to Find the HCF of 272 and 425 by Long Division Method?

To find the HCF of 272, 425 using long division method, 425 is divided by 272. The corresponding divisor (17) when remainder equals 0 is taken as HCF.

If the HCF of 425 and 272 is 17, Find its LCM.

HCF(425, 272) × LCM(425, 272) = 425 × 272
Since the HCF of 425 and 272 = 17
⇒ 17 × LCM(425, 272) = 115600
Therefore, LCM = 6800
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 272 and 425?

There are three commonly used methods to find the HCF of 272 and 425.

By Listing Common Factors
By Long Division
By Prime Factorization

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