Find the HCF of the following by using Euclid division lemma.
(i) 50 and 70
(ii) 96 and 72
(iii) 300 and 550
(iv) 1860 and 2015
Answers
Answer:
Euclid division lemma :-
a = bq + r
0 ≤ r < b
a > b
(i)50 and 70
70 = 50 × 1 + 20
50 = 20 × 2 + 10
20 = 10 × 2 + 0
As the remainder is equal to zero, we can not proceed further.
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
As the remainder is zero,we can not proceed further.
HCF (96,62) = 2
(iii)300 and 550
550 = 300 × 1 + 250
300 = 250 × 1 + 50
250 = 50 × 5 + 0
As the remainder is equal to zero,we can not proceed further.
HCF (300,550) = 50
(iv) 1860 and 2015
2015 = 1860 × 1 + 155
1860 = 155 × 12 + 0
As the remainder is equal to zero, we can not proceed further.
HCF (1860,2015) = 155
Hope it helps.
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i) 50 and 70
70=1x50+20
50=20x2+10
20=10x2+0
HCF=10
ii)96 and 72
96=72x1+24
72=24x3+0
HCF=24
iii)300 and 550
550=300x1+250
300=250x1+50
HCF=250
iv)1860 and 2015
2015=1860x1+155
1860=155x12+0
HCF=155