Question

Ravi wrote two digits of a 3-digit number on the blackboard as shown below. Find the missing digit, if it has factor 11 and 13 as factors?

1

?

3

A. 2
B. 4
C. 6
D. 8

Answer 1

Hint: We want to find the missing number between 1 and 3, which will make the number factor of both 11 and 13. Hence, both 11 and 13 should divide the number completely. Since the numbers 11 and 13 are prime, their product will be the number divided by 11 and 13. Then, compare with the given digits to find the missing digit.

Complete step by step answer:

We have to find a digit such that when that digit is placed between 1 and 3, the number becomes the factor of 11 and 13.
Since 11 and 13 are prime numbers, that is they do not have any other factor except for 1 and the number itself.
Therefore, the number which has 11 and 13 as factors will be the product of the two numbers.
Therefore, find the product of 11 and 13
$11 \times 13 = 143$
Thus, 143 is a number that is divisible by both 11 and 13.
But, on the board, Ravi has already written 1 and 3 and the missing number between them will be 4.
Hence, option B is correct.

Note: Factors of a given are the numbers that divide the completely. Prime numbers have only two factors. Here, 143 is also the LCM of the numbers 11 and 13. That is, if numbers are prime, the LCM is the product of those numbers and HCF is those numbers is 1.