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Q.

If the HCF of 408 and 1032 is expressible in the form 1032m−408×5  , find  m.


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a

3

b

4

c

2

d

5 

answer is C.

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Detailed Solution

Given integers 408 and 1032 and HCF(408, 1032) is expressible in the form of 1032m−408×5.  
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 408, 1032
1032=408×2+216……(1)   ∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 408 and remainder 216
408=216×1+192…….(2)  
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 216 and remainder 192
216=192×1+24...............(3)  
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 192 and remainder 24
192=24×8+0  
∴  remainder = 0  
∴  HCF of 1032, 408 is 24.
Given that HCF=1032m−408×5  
24 =1032 m−408×5 24 =1032 m−2040 1032 m =24+2040 1032 m =2064  m = 2064 1032 m =2  
Therefore, value of m is 2.
Hence the correct option is 3.
 
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If the HCF of 408 and 1032 is expressible in the form 1032m−408×5  , find  m.