Prime numbers below 100 — Mathematics, 11–13
Primes are the numbers with only two divisors: find the 25 below 100 and use them to solve problems.
Prime numbers: exactly two divisors
A prime number has only 1 and itself as divisors: 7 divides exactly only by 1 and by 7. The number 1 is not prime: it has just one divisor. The number 2 is prime (1 and 2) and it is the only even prime. There are 25 prime numbers less than 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.
Why 18 cards share out easily and 19 do not
Deal 18 cards equally and it works for 1, 2, 3, 6, 9 or 18 players, with none left over. With 19 cards it only works for 1 player or for 19: 19 is prime. Squared paper shows the same: with 18 squares you can build the rectangles 1 × 18, 2 × 9 and 3 × 6; with 19 you only get 1 × 19, a single row. A prime number can only be arranged in one row: it makes no rectangle with both sides bigger than 1.
Finding the primes up to 100: cross out multiples
Write the numbers from 2 to 100. Keep 2 and cross out its multiples (4, 6, 8…). Move to the first number not crossed out, 3: keep it and cross out the multiples of 3 (9, 15, 21…). Do the same with 5 and with 7. Why stop at 7? The next multiple of 11 that would not be crossed out already is 11 × 11 = 121, which is over 100. What is left are the primes: 25 numbers, from 2 to 97.
The trap: ‘if it is odd, it is prime’
A reasonable mistake: since even numbers (except 2) have 2 as a divisor, you think every odd number is prime. It is not so: 51 = 3 × 17, 57 = 3 × 19 and 91 = 7 × 13 look prime and are not. To test a number bigger than 7 and smaller than 100, check whether 2, 3, 5 or 7 divides it; if none does, it is prime. Also remember: 1 is not prime, and 2 is prime although it is an even number.
Where you see primes outside school
Thirteen chairs can only be set out in one row of 13 (or 13 rows of one): 13 is prime. So with 13 people you cannot make several equal teams of more than one person; with 12 you can, in several ways. Sharing material among groups, splitting a class into teams, setting out rows: it is always a question about divisors. Prime numbers also protect information: online security uses very large primes.
Keep exploring
Other languages
Loading MyLeoNes™…