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Q.

Only the numbers 3, 5, 15, 25, and 75 can be used to divide the numbers 525 and 3000. What is HCF (525, 3000)? Justify your answer.


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a

75

b

65

c

15

d

30 

answer is A.

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Detailed Solution

It is given that, only the numbers 3, 5, 15, 25, and 75 can be used to divide the numbers 525 and 3000.
Euclid's lemma will enable us to determine the HCF of 525,3000 .   ⇒3000=525×5+375 ⇒525=150×2+75 ⇒150=75×2+0  
Therefore, HCF 525,3000 =75.  
Also, the factors 525 and 3000 are 3, 5, 15, 25, and 75.
Hence, the highest common factor is 75.
525 and 3000 have 75 as their highest common factor.
Therefore, the correct option is 1.
 
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