GATE CS 2015 Set 2 — Question 14
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Engineering Mathematics → Sets & Combinatorics → Permutations & Combinations
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Question
The number of divisors of 2100 is _________
Correct answer
36 to 36
Solution
To find the number of divisors of 2100, we first find the prime factorization of 2100.
So, If a number has a prime factorization , then the number of divisors of is given by the product of one more than each exponent:
Number of divisors For :
(for prime 2)
(for prime 3)
(for prime 5)
(for prime 7)Number of divisors
Thus, the number of divisors of 2100 is 36.
So, If a number has a prime factorization , then the number of divisors of is given by the product of one more than each exponent:
Number of divisors For :
(for prime 2)
(for prime 3)
(for prime 5)
(for prime 7)Number of divisors
Thus, the number of divisors of 2100 is 36.
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