211
- = x 0 1 2 3 4 5 6 7 8 9 ( ) % < > + - = x 0 1 2 3 4 5 6 7 8 9 ( )
% < > + - = x 0 1 2 3 4 5 6 7 8 9 ( ) % < > + - = x 0 1 2 3 4 5 6 7 8 9
( ) % < > + - = x 0 1 2 3 4 5 6 7 8 9 ( ) % < > + - = x 0 1 2 3 4 5 6 7 8
9 ( ) % < > + - = x 0 1 2 3 4 5 6 7 8 9 ( ) % < > + - = x 0 1 2 3 4 5 6 7
8 9 ( ) % < > + - = x 0 1 2 3 4 5 6 7 8 9 ( ) % < > + - = x 0 1 2 3 4 5 6
7 8 9 ( ) % < > + - = x 0 1 2 3 4 5 6 7 8 9 ( ) % < > + - = x 0 1 2 3 4 5
6 7 8 9 ( ) % < > + - = x 0 1 2 3 4 5 6 7 8 9 ( ) % < > + - = x 0 1 2 3
AAppendix Dppendix D
T TESTS FOR ESTS FOR
DDIVISIBILITYIVISIBILITY
It is often useful to know whether a number is evenly divisible by
another number. Here are some ways you can fi nd out without
doing a full division.
Divisibility by 2: All even numbers are divisible by 2; that is, all
whole numbers for which the fi nal digit is 0, 2, 4, 6 or 8.
Divisibility by 3: If the sum of the digits is divisible by 3, then the
number is also divisible by 3. For instance, the digit sum of 45 is 9
(4 + 5 = 9), which is divisible by 3, so 45 is divisible by 3.
Divisibility by 4: If the last two digits are divisible by 4, the number
is divisible by 4. Th is is because 100 is evenly divisible by 4 (100 =
4 × 25).
Th ere is an easy shortcut. Don’t worry how long the number is; if
the tens digit is even, forget it and check if the units digit is divisible
by 4. (It must be 4 or 8.) If the tens digit is odd, carry 1 to the units
digit and check if it is divisible by 4. Th at is because 20 is evenly
divisible by 4 (4 × 5 = 20).
bbapp04.indd 211app 04 .indd 211 1 1/5/07 11:36:17 AM/ 5 / 07 11 : 36 : 17 AM
- = x 0 1 2 3 4 5 6 7 8 9 ( ) % < > + - = x 0 1 2 3 4 5 6 7 8 9 ( )