Question

find the hcf of the following by using Euclid division lemma. 1)50 and 70; 2)96 and 72; 3)300 and 550 ; 4) 1860 and 2015​

Answer 1

Question :-

find the hcf of the following by using Euclid division lemma. 1)50 and 70; 2)96 and 72; 3)300 and 550 ; 4) 1860 and 2015

Answer :-

(i)50 and 70

⇒ 70 = 50 × 1 + 20

⇒ 50 = 20 × 2 + 10

⇒ 20 = 10 × 2 + 0

• HCF (50,70) = 10

(ii)96 and 62

⇒ 96 = 62 × 1 + 34

⇒ 62 = 34 × 1 + 28

⇒ 34 = 28 × 1 + 6

⇒ 28 = 6 × 4 + 4

⇒ 6 = 4 × 1 + 2

⇒ 4 = 2 × 2 + 0

• HCF (96,62) = 2

(iii)300 and 550

⇒ 550 = 300 × 1 + 250

⇒ 300 = 250 × 1 + 50

⇒ 250 = 50 × 5 + 0

• HCF (300,550) = 50

(iv) 1860 and 2015

⇒ 2015 = 1860 × 1 + 155

⇒ 1860 = 155 × 12 + 0

• HCF (1860,2015) = 155

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➤ Extra shots :-

What's the Euclid division lemma is ?

Euclid division lemma :-

• a = bq + r

0 ≤ r < b

$a$ > b

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Answer 2

Answer:

(i)50 and 70

⇒ 70 = 50 × 1 + 20

⇒ 50 = 20 × 2 + 10

⇒ 20 = 10 × 2 + 0

HCF (50,70) = 10

(ii)96 and 62

⇒ 96 = 62 × 1 + 34

⇒ 62 = 34 × 1 + 28

⇒ 34 = 28 × 1 + 6

⇒ 28 = 6 × 4 + 4

⇒ 6 = 4 × 1 + 2

⇒ 4 = 2 × 2 + 0

HCF (96,62) = 2

(iii)300 and 550

⇒ 550 = 300 × 1 + 250

⇒ 300 = 250 × 1 + 50

⇒ 250 = 50 × 5 + 0

HCF (300,550) = 50

(iv) 1860 and 2015

⇒ 2015 = 1860 × 1 + 155

⇒ 1860 = 155 × 12 + 0

HCF (1860,2015) = 155

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Step-by-step explanation:

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