Chapter 4: Factors and Multiples 47MATH TRAP
Most people think 1 is a prime number. Most people are wrong. It’s understandable.
The number 1 has no other factors, but it doesn’t quite fit the definition of prime. Its
factors aren’t itself and 1. They’re itself and itself, or 1 and 1. It’s sort of strange, but it
gets its own category. The number 1 is neither prime nor composite. It’s called a unit.Finding Prime Numbers
Take a look at the following chart, which shows the whole numbers 1 through 50. You know 2 is
prime, because its only factors are 2 and 1, but all the other even numbers have 2 as a factor, so
they’re composite. Multiples of 2 can be blocked out.
The number 3 is prime, but all multiples of 3 are composite, and 5 is prime, but any other
number that ends in 5 is composite because it’s divisible by 5. All the multiples of 3 or 5 that
haven’t already been eliminated can be blocked out.
The numbers 4 and 6 have already been marked as composite, but 7 is prime. Several multiples
of 7 have already been eliminated as composite. You just need to mark 7 v 7, or 49, as composite,
and believe it or not, everything left is prime, except for 1, which is in a class by itself. That
means 16 of the first 50 counting numbers are prime.12 34 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 4 0
41 42 43 4 4 45 46 47 48 49 50WORLDLY WISDOM
As the numbers get bigger, prime numbers become fewer and more spread out,
but mathematicians are still finding them. The largest known prime number is
257 ,885,161− 1 , a number with 17,425,170 digits.How do you know if a large number is prime? You won’t need to worry about extremely large
numbers with thousands of digits, but you may need to know about numbers in the hundreds or
thousands. Is 136 prime? How about 2,485? What about 901?
Sometimes it’s easy to tell. The number 136 can’t be prime because it’s even, so it has 2 as a factor
as well as itself and 1. In the same way, 2,485 ends in 5, so it’s divisible by 5 and therefore not
prime. The number 901 is harder. It’s not even, and it’s not a multiple of 5, because it doesn’t end
in 5 or 0, but what about other numbers? Does it have any divisors?