Four prime numbers are written in ascending order of their magnitude. The product of the first three is 715 and that of the last three is 2431. What is the largest given prime number?

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Solution

The correct option is C 17
Let the four prime numbers be a, b, c and d
According to the question
$a \times b \times c = 715$ and
$b \times c \times d = 2431$
$H C F o f (a b c a n d b c d) = b c$
$∴ 715 = 11 \times 13 \times 5 a n d 2431 = 11 \times 13 \times 17$
HCF of 715 and 2431 $= 11 \times 13 = 143$
$∴ L a r g e s t n u m b e r (d) = \frac{b c d}{b c} = \frac{2431}{143} = 17$

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Four prime numbers are written in ascending order of their magnitude. The product of the first three is 715 and that of the last three is 2431. What is the largest given prime number?

The correct option is C 17Let the four prime numbers be a, b, c and dAccording to the question a×b×c=715and b×c×d=2431 HCFof(abcandbcd)=bc∴715=11×13×5and2431=11×13×17 HCF of 715 and 2431 =11×13=143∴Largestnumber(d)=bcdbc=2431143=17