A natural number n divides 732 and leaves 12 as a remainder. How many values of n are possible?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 20.
If n divides 732 and leaves a remainder of 12
So, 732 - 12 = 720 is perfectly divisible by n
720 = 24 × 32 × 5
Number of factors = (4 + 1) × (2 + 1) × (1+1) = 5 × 3 × 2 = 30
Since the remainder is 12, n must be greater than 12.
We need to exclude the factors of 720 that are less than or equal to 12.
These factors are 1, 2, 3, 4, 5, 6, 8, 9, 10, and 12 (10 factors)
Remaining factors = 30 - 10 = 20.
Therefore, there are 20 possible values of n.