Question

There are 4 prime numbers written in ascending order . The product of the first 3 is 385 , and the product of the last 3 is 1001 . The last number is :
A. 11
B. 13
C. 17
D .19

Answer 1

Hint: Try to think of where factorizing would get you , in this problem .
What will do is factorize both 385 and 1001 into their prime factors . Naturally , we will get 3 prime factors for each because it is their multiplication that has formed these numbers . Then we will arrange those prime factors in ascending order to find the largest prime number .

Complete step-by-step answer:
Now we will factorize both the numbers
Prime factorization of 385 is : $5\, \times \,7\, \times \,11$
Prime factorization of 1001 is : $7\, \times \,11\, \times 13$
Arranging in ascending order , the 4 prime numbers are
     \[5\,,\,7\,,\,11\,,\,13\]

Therefore , the last number is 13 . Option B is correct .

Note: Make sure to eliminate the prime factors that are appearing in both numbers . In this case , 7 and 11 are common , so count them only once because the question asks for 4 distinct prime numbers.