The number of divisors of 2100 is _____ .
2015
The number of divisors of 2100 is _____ .
Attempted by 9 students.
Show answer & explanation
Correct answer: 36
Prime factorization: 2100 = 2^2 × 3^1 × 5^2 × 7^1.
Number of divisors formula: If n = p1^a × p2^b × ... then the number of positive divisors of n is (a+1)(b+1)...
Apply the formula to the exponents 2, 1, 2, 1: compute (2+1) × (1+1) × (2+1) × (1+1).
Multiply: 3 × 2 × 3 × 2 = 36.
Therefore, the number of positive divisors of 2100 is 36.