UNCORRECTEDSAMPLEPAGES

Another way of representing this information is 27 = 4 × 6 + 3

■ Key terms

• Dividend The starting number; the total; the amount you have

• Divisor The number doing the dividing; the number of groups

• Quotient The number of times the divisor went into the dividend, also known as ‘the answer’ to a division calculation

• Remainder The number left over; the number remaining (sometimes written as ‘rem.’)

■ Divisibility tests

1 All numbers are divisible by 1

2 All even numbers are divisible by 2. Last digit must be a 0, 2, 4, 6 or 8

3 The sum of the digits must be divisible by 3.

4 The number formed from the last two digits must be divisible by 4.

5 The last digit must be a 0 or 5.

6 Must pass the divisibility tests for 2 and 3

7 (There is no easy test for divisibility by 7.)

8 The number formed from the last three digits must be divisible by 8

9 The sum of the digits must be divisible by 9

10 The last digit must be 0.

Building Understanding

1 Give a reason why: a 8631 is not divisible by 2 c 426 is not divisible by 4 e 87 548 is not divisible by 6 g 3 333 333 is not divisible by 9

2 Give the remainder when: a 326 is divided by 3 c 72 is divided into six groups b 31 313 is not divisible by 3 d 5044 is not divisible by 5 f 214 125 is not divisible by 8 h 56 405 is not divisible by 10 b 21 154 is divided into groups of four d 45 675 is shared into five groups

3 Which three divisibility tests involve calculating the sum of the digits?

4 If you saw only the last digit of a 10-digit number, which three divisibility tests (apart from 1) could you still apply ?

Example 6 Applying divisibility tests

Determine whether or not the following calculations are possible without leaving a remainder.

a 54 327 ÷ 3 b 765 146 ÷ 8

SOLUTION EXPLANATION