NTA PhD Entrance Examination CS 2023| Part 2 Question: 1

Question

Question No. 1 / Question ID 974051
Marks: 4.00

The number of divisors of 2100 is
1. 42
2. 36
3. 78
4. 72
1 (Chosen Option)
2
3
4

Answer 1

Answer: option(2) 36

To find the number of divisors of 2100, you can prime factorize the number and then use the exponents of the prime factors to calculate the number of divisors.

Prime factorization of 2100 = 2²×3×5²×7.

Now, to find the number of divisors, add 1 to each exponent in the prime factorization and then multiply the results together:

No. of divisors = (2+1)×(1+1)×(2+1)×(1+1)

                           = 3×2×3×2

                           =36

So, the number of divisors of 2100 is 36.