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34 vote

The HCF of two numbers is 12 and their sum is 384. How many such pairs of numbers are possible?

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The HCF of two numbers is 12 and their sum is 384. How many such pairs of numbers are possible?
1). 8
2). 7
3). 9
4). 4


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1 answers

27 vote
Answered by on | Votes 27 |

As both the numbers have the highest common factor 12 it clearly means that the both the numbers are the multiples if 12

So let the numbers be 12x and 12y

As given their sum is 384

ATQ,12x+12y=384

12 (x+y)=384

x+y=32

So the number of pairs with 32 as their sum are (1,31),(2,30) ..... (16,16)

Hence 16 such pairs are possible

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