Page 14 - Mathematics Coursebook

1.4 Factors and tests for divisibility

Divisible by 7 !ere is no simple test for 7. Sorry!
Divisible by 8 A number is divisible by 8 if its last three digits form a number that is divisible by 8.
Example 17 816 is divisible by 8 because 816 is. 816 ÷ 8 = 102 with no remainder.
Divisible by 9 Add the digits. If the sum is divisible by 9, so is the original number. !is is similar to

the test for divisibility by 3.

Example !e number 6786, used for divisibility by 3, is also divisible by 9.
Divisibility by Multiples of 10 end with 0. Multiples of 100 end with 00.
10 or 100

) Exercise 1.4

1 The number 18 has six factors. Two of these factors are 1 and 18.
Find the other four.
2 Find all the factors of each of each number.
a 10 b 28 c 27 d 44
e 11 f 30 g 16 h 32
3 The number 95 has four factors. What are they?

4 One of the numbers in the box is different from the rest.
Which one, and why? 13 17 21 23 29
5 The numbers 4 and 9 both have exactly three factors.
Find two more numbers that have exactly three factors. Think about the factors of 4 and 9.
6 Find the common factors of each pair of numbers.
a 6 and 10 b 20 and 25 c 8 and 15
d 8 and 24 e 12 and 18 f 20 and 50
7 There is one number less than 30 that has eight factors.
There is one number less than 50 that has ten factors.
Find these two numbers.
8 a Find a number with four factors, all of which are odd numbers.
b Find a number with six factors, all of which are odd numbers.

9 Use a divisibility test to decide which of the numbers in the box: 421 222 594 12 345 67 554
a is a multiple of 3 b is a multiple of 6
c is a multiple of 9 d has 5 as a factor.
10 a Which of the numbers in the box:
i is a multiple of 10 ii has 2 as a factor 55 808 55 810 55 812
iii has 4 as a factor iv is a multiple of 8? 55 814 55 816 55 818
b If the sequence continues, what will be the first multiple of 100?

1 Integers 13