How many prime numbers are there between 80 and 105?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5
A number up to 105 that is not prime must have a factor no bigger than \(\sqrt{105}\approx10.2\), so it is enough to test each odd number for divisibility by 3, 5 and 7.
Divisible by 3: 81, 87, 93, 99
Divisible by 5: 85, 95
Divisible by 7: 91 (\(7\times13\))
Left over, the primes: 83, 89, 97, 101, 103, that is, 5 primes
Tip: To test whether a number is prime, divide it only by the primes up to its square root. 91 looks prime but is \(7\times13\).