![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Find the HCF of the following numbers using the prime factorisation method.
a. 16 and 30
b. 15 and 20
c. 45 and 58
d. 124 and 26
e. 36 and 27
Given:
a. 16 and 30
b. 15 and 20
c. 45 and 58
d. 124 and 26
e. 36 and 27
To do:
We have to find the HCF of the given integers by applying the prime factorization method.
Solution:
We can find the HCF of given numbers by writing the numbers as a product of their prime factors and multiplying all common prime factors.
(a) Prime factorisation of 16:
- $2\ \times\ 2\ \times\ 2\ \times\ 2\ =\ 2^4$
Prime factorisation of 30:
- $2\ \times\ 3\ \times\ 5\ =\ 2^1\ \times\ 3^1\ \times\ 5^1$
Multiplying all common prime factors:
$2^1\ =\ 2$
HCF(16, 30) $=$ 2
The HCF of 16 and 30 is 2.
Similarly,
(b) $15=3\times5=3^1\times5^1$
$20=2\times2\times5=2^2\times5^1$
HCF (15, 20) $=5^1=5$
(c) $45=3\times3\times5=3^2\times5^1$
$58=2\times29=2^1\times29^1$
HCF (45, 58) $=1$
(d) $124=2\times2\times31=2^2\times31^1$
$26=2\times13=2^1\times13^1$
HCF (124, 26) $=2^1=2$
(e) $36=2\times2\times3\times3=2^2\times3^2$
$27=3\times3\times3=3^3$
HCF (36, 27) $=3^2=9$