Question

Find the HCF of the numbers by prime factorization and continued division method 12 and 15​

Answer 1

$\red{\underline{\underline{\sf{Given:}}}}$

Two numbers = 12, 15

$\red{\underline{\underline{\sf{To\:\:be\:\:found:}}}}$

HCF of 12 and 15.

Prime factorisation of 12

$\begin{array}{r | l}2 & 12\\\cline{2-2} 2 & 6\\\cline{2-2} 3 & 3\\\cline{2-2} & 1 \\\end{array}\:\:\: \rightarrow \boxed{ 12 = 2^{2} \times 3}$

Prime factorisation of 15

$\begin{array}{r | l}3 & 15\\\cline{2-2} 5 & 5\\\cline{2-2} & 1\ \\ \end{array}\:\:\: \rightarrow \boxed{ 15 = 3 \times 5}$

So,

12 = 2² × 3

15 = 3 × 5

Now,

HCF = Highest Common Factor

[Tip for HCF - Find the common and write its lowest power]

Common in 12, 15 = 3

so,

$\red{\boxed{\sf{HCF(12, 15) = 3}}}$

$\rule{200}2$

Division method

$\bf . \:\:\:\:\:\:\: 1 \\ .\:\:\:\:\rule{30}1 \\ 12\bigg) 15 \\.\:\: -12 \\ .\:\:\:\: \rule{70}1 \\. \:\:\:\:\:\:\:\:\: 3 \:\:\:\:\:\:\: \bigg) 12 \:\:\:\:\: \bigg(4 \\ . \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: - 12 \\ . \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \rule{40}1 \\ . \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \:\:\: \:0$

so,

15 = 12 × 1 + 3

12 = $\red{\sf{3}}$ × 4 + 0

Here remainder is 0

Hence,

3 is the HCF of 12, 15