Question

Solve the following question and mark the best possible option.
How many numbers are co-prime to 4608 that lies between 1000 and 2000, both inclusive?

विकल्प

• 249

• 332

• 166

• 334

Answer 1

We have 4608 = 2⁹ × 3². Now all those numbers between 1000 and 2000 which are not multiples of 2 and 3 will be coprime to 4608.
Total numbers between 1000 and 2000 (including 1000 and 2000) = 1001.
Out of which 501 are even numbers and remaining500 are odd numbers.
Now out of these 500 numbers, every third number is a multiple of 3.
So there are `500/3` = 166 multiples of 3.
Hence the total numbers between 1000 and 2000 which are co-prime to 4608 are = 1001 – 501 – 166 = 334.