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HCF of 65 and 117

HCF of 65 and 117 is the largest possible number that divides 65 and 117 exactly without any remainder. The factors of 65 and 117 are 1, 5, 13, 65 and 1, 3, 9, 13, 39, 117 respectively. There are 3 commonly used methods to find the HCF of 65 and 117 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 65 and 117
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 65 and 117?

Answer: HCF of 65 and 117 is 13.

Explanation:

The HCF of two non-zero integers, x(65) and y(117), is the highest positive integer m(13) that divides both x(65) and y(117) without any remainder.

Methods to Find HCF of 65 and 117

The methods to find the HCF of 65 and 117 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

HCF of 65 and 117 by Prime Factorization

Prime factorization of 65 and 117 is (5 × 13) and (3 × 3 × 13) respectively. As visible, 65 and 117 have only one common prime factor i.e. 13. Hence, the HCF of 65 and 117 is 13.

HCF of 65 and 117 by Long Division

HCF of 65 and 117 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 117 (larger number) by 65 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (65) by the remainder (52).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (13) is the HCF of 65 and 117.

HCF of 65 and 117 by Listing Common Factors

Factors of 65: 1, 5, 13, 65
Factors of 117: 1, 3, 9, 13, 39, 117

There are 2 common factors of 65 and 117, that are 1 and 13. Therefore, the highest common factor of 65 and 117 is 13.

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HCF of 65 and 117 Examples

Example 1: Find the highest number that divides 65 and 117 exactly.

Solution:

The highest number that divides 65 and 117 exactly is their highest common factor, i.e. HCF of 65 and 117.
⇒ Factors of 65 and 117:
- Factors of 65 = 1, 5, 13, 65
- Factors of 117 = 1, 3, 9, 13, 39, 117
Therefore, the HCF of 65 and 117 is 13.
Example 2: The product of two numbers is 7605. If their HCF is 13, what is their LCM?

Solution:

Given: HCF = 13 and product of numbers = 7605
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 7605/13
Therefore, the LCM is 585.
Example 3: For two numbers, HCF = 13 and LCM = 585. If one number is 117, find the other number.

Solution:

Given: HCF (z, 117) = 13 and LCM (z, 117) = 585
∵ HCF × LCM = 117 × (z)
⇒ z = (HCF × LCM)/117
⇒ z = (13 × 585)/117
⇒ z = 65
Therefore, the other number is 65.

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FAQs on HCF of 65 and 117

What is the HCF of 65 and 117?

The HCF of 65 and 117 is 13. To calculate the Highest common factor (HCF) of 65 and 117, we need to factor each number (factors of 65 = 1, 5, 13, 65; factors of 117 = 1, 3, 9, 13, 39, 117) and choose the highest factor that exactly divides both 65 and 117, i.e., 13.

What is the Relation Between LCM and HCF of 65, 117?

The following equation can be used to express the relation between Least Common Multiple and HCF of 65 and 117, i.e. HCF × LCM = 65 × 117.

If the HCF of 117 and 65 is 13, Find its LCM.

HCF(117, 65) × LCM(117, 65) = 117 × 65
Since the HCF of 117 and 65 = 13
⇒ 13 × LCM(117, 65) = 7605
Therefore, LCM = 585
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How to Find the HCF of 65 and 117 by Prime Factorization?

To find the HCF of 65 and 117, we will find the prime factorization of the given numbers, i.e. 65 = 5 × 13; 117 = 3 × 3 × 13.
⇒ Since 13 is the only common prime factor of 65 and 117. Hence, HCF (65, 117) = 13.
☛ What is a Prime Number?

What are the Methods to Find HCF of 65 and 117?

There are three commonly used methods to find the HCF of 65 and 117.

By Long Division
By Listing Common Factors
By Prime Factorization

How to Find the HCF of 65 and 117 by Long Division Method?

To find the HCF of 65, 117 using long division method, 117 is divided by 65. The corresponding divisor (13) when remainder equals 0 is taken as HCF.

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