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

**Key Concepts**

Number theory

Algebra

Prime numbers

## Check the Answer

But try the problem first…

Answer: 16

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.

## Other useful links

- https://www.cheenta.com/linear-equations-amc-8-2007problem-20/
- https://www.youtube.com/watch?v=5fWkdSs5PZk

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