Question

There are three numbers which are formed by product of twin primes. if the product of three numbers is 75075 then find these numbers.

Answer 1

The 3 numbers are : 143, 35, 15

From 1-100 all prime numbers are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Twin prime numbers are the pair of numbers which are 2 less or 2 more than another prime number.

Twin prime numbers :

(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73)

The 3 numbers are the twin prime numbers and thier product is 75075

Now, since the number 75075 has 5 in it, there should be atleast one 5

so taking (3,5)= 15  [First Number]

dividing 75075 by 15, we get 5005 which ends with 5

hence it can be concluded that the divisibility will be agan by 5 .

so we have to take (5,7)= 35 [Second Number]

there is no other twin prime number which contains 5.

dividing 5005 by 35 we get 143 which if we look closely is nothing but (11,13)=143

hence the 3 numbers are

(3,5) = 15

(5,7)= 35

(11,13)= 143

143 x 35 x 15 = 75075