Four prime numbers are listed in order. If the product of the first three is 105 and the product of the last three is 385, what is the largest prime number?
11
Let the four primes in order be a, b, c, d, with \(a \times b \times c = 105\) and \(b \times c \times d = 385\).
Factorising, \(105 = 3 \times 5 \times 7\), so a, b, c are 3, 5, 7 in some order.
Factorising, \(385 = 5 \times 7 \times 11\), so b, c, d are 5, 7, 11 in some order.
The common terms b and c must be 5 and 7, which fixes \(a = 3\) and \(d = 11\).
So the four primes in order are 3, 5, 7, 11.
Hence, the largest prime number is 11.
Similar Questions
- The number of prime numbers lying between 389 and 403, both included, is:
- The number of prime numbers lying between 488 and 494, both included, is:
- The number of prime numbers lying between 306 and 313, both included, is:
- The sum of the first six prime numbers is:
- Which of the following is a prime number?
- How many prime numbers are there that are less than 50?
- In four consecutive prime numbers, the product of the last three is 7429 and that of the first three is 4199. The largest of these prime number is:
- The sum of the first four prime numbers is:
- How many of the integers between $109$ and $121$, both inclusive, are prime numbers?
- If $a : b = 3 : 4$ and $d : b = 4 : 3$, then find the ratio of a to d.
Important Questions from Prime Numbers
The number whose only factors are 1 and the number itself is called a/an ________ number.
Consider the following numbers :
1. 437
2. 797
3. 1073
How many of the above numbers are prime ?
What are the total prime numbers from 1 to 100?
How many prime numbers are there between 20 and 50?
How many prime numbers are there between 100 and 120?
