Find the prime factorisation of the following numbers using the division method.
a. 240
b. 720
c. 300
d. 480
e. 1240

Given:

a. 240
b. 720
c. 300
d. 480

e. 1240

To do:

We have to find the prime factorisation of the given numbers using the division method.

Solution:

Factorization by Division method: In this method of factorization, the number is divide by the smallest prime number which divides the given number exactly. Then the quotient is again divided by the smallest or next smallest prime number and the process continues till the quotient gets undividable.

(a) $\frac{240}{2}=120$

$\frac{120}{2}=60$

$\frac{60}{2}=30$

$\frac{30}{2}=15$
$\frac{15}{3}=5$ 

$\frac{5}{5}=1$ 

Therefore,

$240=2\times2\times2\times3\times5$

(b) $\frac{720}{2}=360$

$\frac{360}{2}=180$

$\frac{180}{2}=90$

$\frac{90}{2}=45$
$\frac{45}{3}=15$

 $\frac{15}{3}=5$

$\frac{5}{5}=1$ 

Therefore,

$720=2\times2\times2\times2\times3\times3\times5$

(c) $\frac{300}{2}=150$

$\frac{150}{2}=75$

$\frac{75}{3}=25$

$\frac{25}{5}=5$

$\frac{5}{5}=1$ 

Therefore,

$300=2\times2\times3\times5\times5$

(d) $\frac{480}{2}=240$

$\frac{240}{2}=120$

$\frac{120}{2}=60$

$\frac{60}{2}=30$
$\frac{30}{2}=15$

 $\frac{15}{3}=5$

$\frac{5}{5}=1$ 

Therefore,

$480=2\times2\times2\times2\times2\times3\times5$

(e) $\frac{1240}{2}=620$

$\frac{620}{2}=310$

$\frac{310}{2}=155$

$\frac{155}{5}=31$

$\frac{31}{31}=1$ 

Therefore,

$1240=2\times2\times2\times5\times31$

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Updated on: 10-Oct-2022

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