Question

Use euclid's division algorithum to find the HCF of 135 and 225?​

Answer 1

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Answer 2

$\underline{\underline{\mathfrak{\green{Answer:-}}}}$

HCF = 45

$\underline{\underline{\mathfrak{\green{Explanation:-}}}}$

Given, no.s are 135 and 225

From Euclid's division algorithm,

$\boxed{\pink{a = bq+r}}$

Step :1

a = 225, b = 135

225 = 135 × 1 + 90

Step :2

a = 135, b = 90

135 = 90 × 1 + 45

step :3

a = 90, b = 45

90 = 45 × 2 + 0

Here, remainder(r) = 0

Therefore, divisor in the last step is the HCF

Hence, HCF = 45

_____________________

$\underline{\underline{\mathfrak{\pink{Verification:-}}}}$

Let us, verify by PF method

135 = 3³ × 5¹

225 = 3² × 5²

Here,

HCF = 3² × 5¹

HCF = 9 × 5

HCF = 45

Hence, HCF of 135 and 225 = 45