Question

1. Use Euclid’s division algorithm to find the HCF of:

i. 135 and 225

ii. 196 and 38220

iii. 867 and 255​

Answer 1

(i) 140

By Taking the LCM of 140, we will get the product of its prime factor.

Therefore, 140 = 2 × 2 × 5 × 7 × 1 = 22×5×7

(ii) 156

By Taking the LCM of 156, we will get the product of its prime factor.

Hence, 156 = 2 × 2 × 13 × 3 × 1 = 22× 13 × 3

(iii) 3825

By Taking the LCM of 3825, we will get the product of its prime factor.

Hence, 3825 = 3 × 3 × 5 × 5 × 17 × 1 = 32×52×17

(iv) 5005

By Taking the LCM of 5005, we will get the product of its prime factor.

Hence, 5005 = 5 × 7 × 11 × 13 × 1 = 5 × 7 × 11 × 13

(v) 7429

By Taking the LCM of 7429, we will get the product of its prime factor.

Hence, 7429 = 17 × 19 × 23 × 1 = 17 × 19 × 23

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Answer 2

Answer:

1. 135 and 225

$225=(135×p)+q.$

$⇒225=(135×1)+90.$

$⇒135=(90×1)+45$

$⇒90=(45×2)+0.$

$∴HCF(135,225)=45.$

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2. 196 and 38220

38220 is higher than the 196, such that the smallest number is taken as divisor and the largest number is taken as dividend. Then by using the Euclid's algorithm, The finding of HCF of 196 and 38220 is solved in the below attachment. The quotient for by dividing 38220 by 196 is 195.

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Consider two numbers 867 and 255, and we need to find the HCF of these numbers.

867 is grater than 255, so we will divide 867 by 225

$867 = 255 × 3 + 102$

Now lets divide 255 by 102

$⇒ 255 = 102 × 2 + 51$

Now divide 102 by 51

$⇒ 102 = 51 × 2 + 0$

Here reminder is zero.

$∴ HCF of (867, 255) = 51$