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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

1 Answer

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Best answer

i) For given two positive integers a > b; 

there exists unique pair of integers q and r satisfying a = bq + r; 0≤r<b.

∴ 70 = 50 × 1 + 20 

Here a = 70, b = 50, q = 1, r = 20. 

Now consider 50, 20 

50 = 20 × 2 + 10 

Here a = 50, b = 20, q = 2, r = 10. 

Now taking 20 and 10. 

20 = 10 × 2 + 0 

Here the remainder is zero. 

∴ 10 is the HCF of 70 and 50.

ii) 96 = 72 × 1 + 24 

72 = 24 × 3 + 0 

∴ HCF = 24

iii) 550 = 300 × 1 + 250 

300 = 250 × 1 + 50 

250 = 50 × 5 + 0 

∴ HCF = 50

iv) 2015 = 1860 × 1 + 155 

1860 = 155 × 12 + 0 

∴ HCF = 155

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