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) $=3^2=9$

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Updated on: 10-Oct-2022

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