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CBSE Class 10 Answered

Find the HCF of 155 and 1385 by Eulcid's Algorithm and express it in a linear combination of two numbers
Asked by piyushmalik024 | 08 May, 2019, 07:25: PM
answered-by-expert Expert Answer
 
 
By applying Euclid's Division Algorithm, we get
 
1385 = 155 × 8 + 145
 
Here the remainder (145) ≠ 0
 
155 = 145 × 1 + 10
 
Here the remainder (10) ≠ 0
 
145 = 10 × 14 + 5
 
Here the remainder (5) ≠ 0
 
10 = 5 × 2 + 0
 
Therefore HCF(155, 1385) = 5
 
Linear combination:
5 = 145 - 10 × 14
   = 145 - (155 - 145 × 1) × 14
   = 145 - 155 × 14 + 145 × 14
   = 145 × 15 - 155 × 14
   = (1385 - 155 × 8)15 - 155 × 14
   = 1385 × 15 - 155 × 120 - 155 × 14
   = 1385 × 15 - 155 × 134
   
Answered by Yasmeen Khan | 09 May, 2019, 10:19: AM
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