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Q.

Find the HCF of 105 and 120.


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a

HCF(105, 120) = 15

b

HCF(105, 120) = 12

c

HCF(105, 120) = 13

d

HCF(105, 120) = 14 

answer is A.

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Detailed Solution

Given to define HCF of two positive integers and to find HCF(105, 120).
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 105, 120
120=105×1+15  
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 105 and remainder 15
105=15×7+0  
∴  remainder = 0.
Therefore, HCF(105, 120) = 15.
Hence the correct option is 1.
 
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