Question

use euclids division algorithim find hcf of 135 and 225
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Answer 1

Answer:

★ HCF = 90 ★

Step-by-step explanation:

Given:

• Numbers are 135 and 225

To Find:

• HCF of 135 and 225 by Euclid's division algorithm

Solution:

★ a = bq + r, 0 ≤ r < b ★

Here, 225 > 135

$\small\implies{\sf }$ 225 = 135 x 1 + 90

$\small\implies{\sf }$ 135 = 90 x 1 + 45

$\small\implies{\sf }$ 90 = 45 x 2 + 0

Hence, HCF of 135 and 225 is 90

Answer 2

$\bf{\underline{\underline{To\:find}}}$

$\mathsf{\star\: \: HCF \:of\:135\:and\: 225}$

$\bf{\underline{\underline{Solution}}}$

$\mathsf{let\:\: a = 225\: \: and\:\: b = 135}$

According to Euclid's division algorithm

$\mathtt{\fbox{\blue{a = bq + r}} \: \:\:\:\:\: where, \: 0 ≤ r < b}$

• a = Dividend
• b = Divisor
• q = Quotient
• r = Remainder

$\mathtt{\implies\: 225 = 135 × 1 + 90}$

$\mathtt{\implies\: 135 = 90 × 1 + 45}$

$\mathtt{\implies\: 90 = 45 × 2 + 0}$

$\huge{\fbox{\mathtt{\green{HCF = 45}}}}$

∴ HCF of 135, 225 = 45

━━━━━━━━━━━━━━━━━━━

$\bf{\underline{\underline{Verification}}}$

By Prime factorisation method

★ 135

$</p><p>\begin{array}{r | 1}</p><p>3 & 135 \\</p><p>\cline{2-2} 3 & 45 \\</p><p>\cline{2-2} 3 & 15 \\</p><p>\cline{2-2} 5 & 5 \\</p><p>\cline{2-2} & 1 \\</p><p>\end{array}</p><p>$

★ 225

$</p><p>\begin{array}{r | 1}</p><p>3 & 225 \\</p><p>\cline{2-2} 3 & 75 \\</p><p>\cline{2-2} 5 & 25 \\</p><p>\cline{2-2} 5 & 5 \\</p><p>\cline{2-2} & 1 \\</p><p>\end{array}</p><p>$

135 = 3 × 3 × 3 × 5 × 1

225 = 3 × 3 × 5 × 5 × 1

HCF = 3 × 3 × 5 × 1

HCF = 45