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HCF of 117 and 221

HCF of 117 and 221 is the largest possible number that divides 117 and 221 exactly without any remainder. The factors of 117 and 221 are 1, 3, 9, 13, 39, 117 and 1, 13, 17, 221 respectively. There are 3 commonly used methods to find the HCF of 117 and 221 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 117 and 221
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 117 and 221?

Answer: HCF of 117 and 221 is 13.

Explanation:

The HCF of two non-zero integers, x(117) and y(221), is the highest positive integer m(13) that divides both x(117) and y(221) without any remainder.

Methods to Find HCF of 117 and 221

Let's look at the different methods for finding the HCF of 117 and 221.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 117 and 221 by Prime Factorization

Prime factorization of 117 and 221 is (3 × 3 × 13) and (13 × 17) respectively. As visible, 117 and 221 have only one common prime factor i.e. 13. Hence, the HCF of 117 and 221 is 13.

HCF of 117 and 221 by Listing Common Factors

Factors of 117: 1, 3, 9, 13, 39, 117
Factors of 221: 1, 13, 17, 221

There are 2 common factors of 117 and 221, that are 1 and 13. Therefore, the highest common factor of 117 and 221 is 13.

HCF of 117 and 221 by Long Division

HCF of 117 and 221 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 221 (larger number) by 117 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (117) by the remainder (104).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (13) is the HCF of 117 and 221.

☛ Also Check:

HCF of 117 and 221 Examples

Example 1: For two numbers, HCF = 13 and LCM = 1989. If one number is 117, find the other number.

Solution:

Given: HCF (y, 117) = 13 and LCM (y, 117) = 1989
∵ HCF × LCM = 117 × (y)
⇒ y = (HCF × LCM)/117
⇒ y = (13 × 1989)/117
⇒ y = 221
Therefore, the other number is 221.
Example 2: The product of two numbers is 25857. If their HCF is 13, what is their LCM?

Solution:

Given: HCF = 13 and product of numbers = 25857
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 25857/13
Therefore, the LCM is 1989.
Example 3: Find the highest number that divides 117 and 221 exactly.

Solution:

The highest number that divides 117 and 221 exactly is their highest common factor, i.e. HCF of 117 and 221.
⇒ Factors of 117 and 221:
- Factors of 117 = 1, 3, 9, 13, 39, 117
- Factors of 221 = 1, 13, 17, 221
Therefore, the HCF of 117 and 221 is 13.

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FAQs on HCF of 117 and 221

What is the HCF of 117 and 221?

The HCF of 117 and 221 is 13. To calculate the HCF of 117 and 221, we need to factor each number (factors of 117 = 1, 3, 9, 13, 39, 117; factors of 221 = 1, 13, 17, 221) and choose the highest factor that exactly divides both 117 and 221, i.e., 13.

How to Find the HCF of 117 and 221 by Prime Factorization?

To find the HCF of 117 and 221, we will find the prime factorization of the given numbers, i.e. 117 = 3 × 3 × 13; 221 = 13 × 17.
⇒ Since 13 is the only common prime factor of 117 and 221. Hence, HCF (117, 221) = 13.
☛ Prime Number

If the HCF of 221 and 117 is 13, Find its LCM.

HCF(221, 117) × LCM(221, 117) = 221 × 117
Since the HCF of 221 and 117 = 13
⇒ 13 × LCM(221, 117) = 25857
Therefore, LCM = 1989
☛ HCF Calculator

What are the Methods to Find HCF of 117 and 221?

There are three commonly used methods to find the HCF of 117 and 221.

By Euclidean Algorithm
By Long Division
By Prime Factorization

What is the Relation Between LCM and HCF of 117, 221?

The following equation can be used to express the relation between LCM and HCF of 117 and 221, i.e. HCF × LCM = 117 × 221.

How to Find the HCF of 117 and 221 by Long Division Method?

To find the HCF of 117, 221 using long division method, 221 is divided by 117. The corresponding divisor (13) when remainder equals 0 is taken as HCF.

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