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
But try the problem first...
Answer: 16
TOMATO, Problem 96
Challenges and Thrills in Pre College Mathematics
First hint
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 ..........
Second Hint
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........
Final Step
for the given case \(3003\) has \(2^4=16 \)divisors.
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