Try this beautiful problem from Integer based on Prime number useful for ISI B.Stat Entrance.
The number of different prime factors of 3003 is.....
Number theory
Algebra
Prime numbers
Answer: 16
TOMATO, Problem 96
Challenges and Thrills in Pre College Mathematics
At first, we have to find out the prime factors. Now \(3003\)=\(3 \times 7 \times 11 \times 13\). but now it can be expressed as another prime number also such as \(3003=3 \times 1001\). So we have to find different prime factors.
Can you now finish the problem ..........
Now, if you have a number and its prime factorisation, \(n={p_1}^{m_1} {p_2}^{m_2}⋯{p_r}^{m_r}\) you can make divisors of the number by taking up to \(m_1\) lots of \(p_1\), up to \(m_2\) lots of \(p_2\) and so on. The number of ways of doing this is going to be\( (m_1+1)(m_2+1)⋯(m_r+1)\).
can you finish the problem........
for the given case \(3003\) has \(2^4=16 \)divisors.
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