The HCF of 65 and 117 is 13. The greatest integer which divides the numbers 65 and 117 evenly is the HCF value. The teachers makes use of simple step-wise explanations, which enhances the problem-solving abilities of students. The factors of 65 are 1, 5, 13, and 65, and the factors of 117 are 1, 3, 9, 13, 39, and 117. The methods to find the HCF are prime factorisation, long division and listing the common factors.
Also read: Highest common factor
What is the HCF of 65 and 117?
The answer to this question is 13. The HCF of 65 and 117 using various methods is given in this article for your reference. The HCF of 65 and 117 is 13, that divides the two numbers, evenly.
How to Find HCF of 65 and 117?
There are three methods to find the HCF of 65 and 117
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 65 and 117 by Prime Factorisation Method
The prime factorisation of 65 and 117 is given by:
65 = 5 × 13
117 = 3 × 3 × 13
Common prime factors of 65 and 117 = 13
Hence, HCF (65, 117) = 13
HCF of 65 and 117 by Long Division Method
We should divide the numbers (65, 117) by their factors to get the HCF using the division method. The HCF of 65 and 117 is the divisor we obtain when the remainder becomes zero after repeated long division.
No further division can be done.
Hence, HCF (65, 117) = 13
HCF of 65 and 117 by Listing the Factors
To calculate the HCF of 65 and 117 by listing out the common factors, list the factors as shown below:
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, and they are 1 and 13.
Therefore, the highest common factor of 65 and 117 is 13.
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Video Lesson on Properties of HCF and LCM
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HCF of 65 and 117 Solved Example
Question: If HCF = 13 and product of two numbers = 7605, find the LCM.
Solution:
Given
HCF = 13
Product = 7605
We know that
HCF × LCM = Product
LCM = Product/HCF
LCM = 7605/13
LCM = 585
Hence, the LCM is 585.
Frequently Asked Questions on HCF of 65 and 117
What is the HCF of 65 and 117?
Find the HCF of 65 and 117 using the long division method.
List the methods used to find HCF of 65 and 117.
If LCM = 585 and HCF = 13 for two numbers, determine the other number when one number is 117.
Consider y as the other number
Given LCM = 585 and HCF = 13
HCF × LCM = 117 × y
y = (HCF × LCM)/ 117
y = (585 × 13)/ 117
y = 65
Therefore, the other number is 65.
Write the relation between HCF and LCM of 65 and 117.
The relation between HCF and LCM of 65 and 117 is
HCF × LCM = 65 × 117
HCF × LCM = 7605
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