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Try this beautiful problem from Integer based on Prime number useful for ISI B.Stat Entrance.

## Prime number | ISI B.Stat Entrance | Problem no. 96

The number of different prime factors of 3003 is…..

• 2
• 15
• 7
• 16

Number theory

Algebra

Prime numbers

## Check the Answer

But try the problem first…

Source

TOMATO, Problem 96

Challenges and Thrills in Pre College Mathematics

## Try with Hints

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.