The HCF of 117 and 221 is 13. The positive integer which can divide 117 and 221 evenly is the HCF of 117 and 221. The factors of 117 are 1, 3, 9, 13, 39, 117, and the factors of 221 are 1, 13, 17, 221. The methods like prime factorisation, long division and listing common factors are used to find the HCF. For a clear-cut idea of the basic concepts of Mathematics, students are advised to refer to this article.
Also read: Highest common factor
What is the HCF of 117 and 221?
The answer to this question is 13. The methods which can be used to find the HCF of given two numbers are discussed in this article. The HCF of 117 and 221 is 13, which divides both 117 and 221 evenly.
How to Find HCF of 117 and 221?
The methods used to find the HCF of 117 and 221 are:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 117 and 221 by Prime Factorisation Method
The prime factorisation of 117 and 221 is:
117 = 3 × 3 × 13
221 = 13 × 17
Common prime factor = 13
Therefore, HCF (117, 221) = 13
HCF of 117 and 221 by Long Division Method
We should divide (117, 221) by their prime factors in order to determine the HCF. The divisor when the remainder is zero after repeated long division is the HCF of 117 and 221.
No further division can be done.
Hence, HCF (117, 221) = 13
HCF of 117 and 221 by Listing Common Factors
The steps to find the HCF of 117 and 221 by listing common factors are provided here:
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, and they are 1 and 13.
Therefore, the highest common factor of 117 and 221 is 13.
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Video Lesson on Properties of HCF and LCM
HCF of 117 and 221 Solved Example
Question: Calculate the HCF of 117 and 221 if the LCM is 1989.
Solution:
Given
LCM = 1989
We know that
HCF × LCM = 117 × 221
HCF = (117 × 221)/1989 = 13
Hence, the HCF is 13.
Frequently Asked Questions on HCF of 117 and 221
What is the HCF of 117 and 221?
To find the HCF, list the factors of 117 and 221.
What methods can we use to find HCF of 117 and 221?
If LCM = 1989 and HCF = 13 for two numbers, determine the other number when one number is 117.
Consider y as the other number
Given LCM = 1989 and HCF = 13
HCF × LCM = 117 x y
y = (HCF × LCM)/117
y = (13 × 1989)/117
y = 221
Therefore, the other number is 221.
If the product of two numbers is 25857 and the HCF is 13, find the LCM.
Given
Product = 25857
HCF = 13
HCF × LCM = Product
LCM = Product/HCF
LCM = 25857/13
LCM = 1989
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