In four consecutive prime numbers that are in | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the four consecutive prime numbers be $a, b, c,$ and $d$ in ascending order,such that $a < b < c < d$.Given that the product of the first thre

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(B) Let the four consecutive prime numbers be $a, b, c,$ and $d$ in ascending order,such that $a Given that the product of the first three is $a 	imes b 	imes c = 385$ and the product of the last three is $b 	imes c 	imes d = 1001$.To find the common factors,we calculate the Highest Common Factor $(HCF)$ of $385$ and $1001$.$385 = 5 	imes 7 	imes 11$$1001 = 7 	imes 11 	imes 13$The common factors are $7$ and $11$,so $b 	imes c = 7 	imes 11 = 77$.Now,using the product of the last three numbers: $b 	imes c 	imes d = 1001$.Substituting $b 	imes c = 77$,we get $77 	imes d = 1001$.Therefore,$d = \frac{1001}{77} = 13$.The four consecutive prime numbers are $5, 7, 11, 13$. The largest prime number is $13$.

In four consecutive prime numbers that are in ascending order,the product of the first three is $385$ and that of the last three is $1001$. The largest given prime number is

Similar Questions

The least number, which when divided by $48, 60, 72, 108$ and $140$ leaves $38, 50, 62, 98$ and $130$ as remainders respectively is

Find the least number which when divided by $16, 18, 20$ and $25$ leaves $4$ as a remainder in each case,but when divided by $7$ leaves no remainder.

The least multiple of $7,$ which leaves a remainder of $4,$ when divided by $6, 9, 15,$ and $18$ is

Two numbers are in the ratio $5:6$. If their $H.C.F.$ is $4$,then their $L.C.M.$ will be

$A$ wholesale tea dealer has $408$ kilograms,$468$ kilograms,and $516$ kilograms of three different qualities of tea. He wants to pack all of it into boxes of equal size without mixing the different qualities. Find the capacity of the largest possible box.

Vedclass Test Series

Exam Paper Generator

Online Exam Module