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Q.

Find the HCF of 155 and 1385.


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a

HCF(155, 1385) = 5

b

HCF(155, 1385) = 4

c

HCF(155, 1385) = 3

d

HCF(155, 1385) = 6 

answer is A.

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Detailed Solution

Given to define HCF of two positive integers and to find HCF(155, 1385).
The highest common factor (HCF) for two or more numbers is the largest number that
divides them.
Euclid's Division Lemma states that if two positive integers a and b exist, then there must be unique values of q and r that satisfy the formula a= bq + r, where  0 ≤ r < b.
Apply Euclid’s division lemma on 155, 1385
1385=155×8+145  
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 155 and remainder 145
155=145×1+10  
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 145 and remainder 10
145=10×14+5  
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 10 and remainder 5
10=5×2+0  
∴  remainder = 0.
Therefore, HCF(155, 1385) = 5.
Hence the correct option is 1.
 
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