Four prime numbers are written in ascending order of their magnitudes.

1.	Four prime numbers are written in ascending order of their magnitudes. The product of the first three is 715 and that of the last three is 2431. What is the largest given prime number ? (a) 5 (b) 19 (c) 17 (d) 23
Answer» Answer is : (c) 17 Let the four prime numbers in the ascending order of their magnitudes be a, b, c and d. Given, a × b × c = 715 and b × c × d = 2431 HCF of (abc and bcd) = bc ∴ Now, 715 = 11 × 13 × 5 and 2431 = 11 × 13 × 17 ⇒ HCF of 715 and 2431 = 11 × 13 = 143 ∴ Largest number (d) = \(\frac{bcd}{bc} = \frac{2431}{143}\) = 17

Four prime numbers are written in ascending order of their magnitudes. The product of the first three is 715 and that of the last three is 2431. What is the largest given prime number ? (a) 5 (b) 19 (c) 17 (d) 23

Answer»

Answer is : (c) 17

Let the four prime numbers in the ascending order of their magnitudes be a, b, c and d.

Given, a × b × c = 715 and b × c × d = 2431

HCF of (abc and bcd) = bc

∴ Now, 715 = 11 × 13 × 5 and 2431 = 11 × 13 × 17

⇒ HCF of 715 and 2431 = 11 × 13 = 143

∴ Largest number (d) = \(\frac{bcd}{bc} = \frac{2431}{143}\) = 17