Exercise · ZW-PRIME-NUMBER-005 · ★☆☆ Basic
To decide whether 97 is prime by trial division, what is the largest prime you must test?
Choose one option.
Show answer
- C. 7
Explanation
It suffices to test primes \(p\le\sqrt{97}\approx9.8\), that is 2, 3, 5 and 7. None divides 97, so it is prime; 11 is unnecessary.
Review the concept: Prime number
A prime number \(p\) is an integer greater than 1 whose only positive divisors are 1 and itself.
\[p>1,\quad d>0,\ d\mid p\ \Rightarrow\ d\in\{1,p\}\]
More practice problems: prime number
- ZW-PRIME-NUMBER-001 Which of these numbers is prime?
- ZW-PRIME-NUMBER-002 How many prime numbers are less than 30?
- ZW-PRIME-NUMBER-003 What is the smallest prime factor of 221?
- ZW-PRIME-NUMBER-004 What is the prime factorization of 360?
- ZW-PRIME-NUMBER-006 Which of these statements about primes is true?
- ZW-PRIME-NUMBER-007 How many positive divisors does 60 have?
- ZW-PRIME-NUMBER-008 What is the smallest prime greater than 100?
- ZW-PRIME-NUMBER-009 If a prime p divides the product ab, what follows?