Page 15 - Cambridge Checkpoint Mathematics Coursebook 7_Slide 02

1.4 Factors and tests for divisibility

Divisible by 7 Th 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. Th is is similar to
the test for divisibility by 3.
Example Th 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

F 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 fi rst multiple of 100?

1 Integers 13