470 ALGEBRA De MYSTiF ieD
DeMYSTiFieD / Algebra DeMYSTiFieD / Gibilisco / 000-0 / AppendixEXAMPLE
126 is even and the sum of its digits is divisible by 9: 1 + 2 + 6 = 9, so 126 is
divisible by 18.
4545 is divisible by 5 and by 9 (4 + 5 + 4 + 5 = 18 and 18 is divisible by 9).To factor a number into its prime factors (those which have no divisors other
than themselves and 1), we start with a list of prime numbers (a short list is
given at the end of this appendix). We begin with the smallest prime number
and keep dividing the prime numbers into the number we want to factor. It
might be that a prime number divides a number more than once. We stop divid-
ing when the square of the prime number is larger than the number. The previ-
ous list of number facts can help us ignore 2 when the number is not even; 5
when does not end in 5; and 3 when the sum of its digits is not divisible by 3.EXAMPLE- 120: The prime numbers to check are 2, 3, 5, 7. The list stops at 7 because
120 is smaller than 11^2 = 121. - 249: The prime numbers to check are 3, 7, 11, 13. The list does not include
2 and 5 because 249 is not even and does not end in 5. The list stops at
13 because 249 is smaller than the next prime number, 17: 17^2 = 289. - 608: The prime numbers to check are 2, 7, 11, 13, 19, 23. The list does not
contain 3 because 6 + 0 + 8 = 14 is not divisible by 3 and does not contain
5 because 608 does not end in 5 or 0. The list stops at 23 because 608 is
smaller than 29^2 = 841. - 342: The prime numbers to check are 2, 3, 7, 11, 13, 17. The list does not
contain 5 because 342 does not end in 5 or 0. The list stops at 17 because
342 is smaller than 19^2 = 361.
EXAMPLE
List the prime numbers to check.- 166
- 401
- 84
- 136
- 465
EXAMPLE
126 is even and the sum of its digits is divisible by 9: 1 + 2 + 6 = 9, so 126 isEXAMPLE- 120: The prime numbers to check are 2, 3, 5, 7. The list stops at 7 because
EXAMPLE
List the prime numbers to check.