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HCF of 85 and 153

HCF of 85 and 153 is the largest possible number that divides 85 and 153 exactly without any remainder. The factors of 85 and 153 are 1, 5, 17, 85 and 1, 3, 9, 17, 51, 153 respectively. There are 3 commonly used methods to find the HCF of 85 and 153 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 85 and 153
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 85 and 153?

Answer: HCF of 85 and 153 is 17.

Explanation:

The HCF of two non-zero integers, x(85) and y(153), is the highest positive integer m(17) that divides both x(85) and y(153) without any remainder.

Methods to Find HCF of 85 and 153

The methods to find the HCF of 85 and 153 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

HCF of 85 and 153 by Long Division

HCF of 85 and 153 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 153 (larger number) by 85 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (85) by the remainder (68).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (17) is the HCF of 85 and 153.

HCF of 85 and 153 by Prime Factorization

Prime factorization of 85 and 153 is (5 × 17) and (3 × 3 × 17) respectively. As visible, 85 and 153 have only one common prime factor i.e. 17. Hence, the HCF of 85 and 153 is 17.

HCF of 85 and 153 by Listing Common Factors

Factors of 85: 1, 5, 17, 85
Factors of 153: 1, 3, 9, 17, 51, 153

There are 2 common factors of 85 and 153, that are 1 and 17. Therefore, the highest common factor of 85 and 153 is 17.

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HCF of 85 and 153 Examples

Example 1: Find the highest number that divides 85 and 153 exactly.

Solution:

The highest number that divides 85 and 153 exactly is their highest common factor, i.e. HCF of 85 and 153.
⇒ Factors of 85 and 153:
- Factors of 85 = 1, 5, 17, 85
- Factors of 153 = 1, 3, 9, 17, 51, 153
Therefore, the HCF of 85 and 153 is 17.
Example 2: For two numbers, HCF = 17 and LCM = 765. If one number is 85, find the other number.

Solution:

Given: HCF (x, 85) = 17 and LCM (x, 85) = 765
∵ HCF × LCM = 85 × (x)
⇒ x = (HCF × LCM)/85
⇒ x = (17 × 765)/85
⇒ x = 153
Therefore, the other number is 153.
Example 3: Find the HCF of 85 and 153, if their LCM is 765.

Solution:

∵ LCM × HCF = 85 × 153
⇒ HCF(85, 153) = (85 × 153)/765 = 17
Therefore, the highest common factor of 85 and 153 is 17.

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FAQs on HCF of 85 and 153

What is the HCF of 85 and 153?

The HCF of 85 and 153 is 17. To calculate the HCF of 85 and 153, we need to factor each number (factors of 85 = 1, 5, 17, 85; factors of 153 = 1, 3, 9, 17, 51, 153) and choose the highest factor that exactly divides both 85 and 153, i.e., 17.

If the HCF of 153 and 85 is 17, Find its LCM.

HCF(153, 85) × LCM(153, 85) = 153 × 85
Since the HCF of 153 and 85 = 17
⇒ 17 × LCM(153, 85) = 13005
Therefore, LCM = 765
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What are the Methods to Find HCF of 85 and 153?

There are three commonly used methods to find the HCF of 85 and 153.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the HCF of 85 and 153 by Long Division Method?

To find the HCF of 85, 153 using long division method, 153 is divided by 85. The corresponding divisor (17) when remainder equals 0 is taken as HCF.

How to Find the HCF of 85 and 153 by Prime Factorization?

To find the HCF of 85 and 153, we will find the prime factorization of the given numbers, i.e. 85 = 5 × 17; 153 = 3 × 3 × 17.
⇒ Since 17 is the only common prime factor of 85 and 153. Hence, HCF (85, 153) = 17.
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What is the Relation Between LCM and HCF of 85, 153?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 85 and 153, i.e. HCF × LCM = 85 × 153.

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