7.1 ANSWERS properties of numbers

Answers

Exercise 1

Write down all divisors of. You may NOT use your calculator.

a) 16

The divisors of 16 are 1, 2, 4, 8 and 16.

16 : 1 = 16 

16 : 2 = 8 

16 : 4 = 4 

16 : 8 = 2 

16 : 16 = 1

 

b) 60

The divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

60 : 1 = 60

60 : 2 = 30

60 : 3 = 20

60 : 4 = 15

60 : 5 = 12 

60 : 6 = 10

60 : 10 = 6 

60 : 12 = 5 

60 : 15 = 4 

60 : 20 = 3 

60 : 30 = 2 

60 : 60 = 1 

Exercise 2

Check whether these numbers are divisible by 3, 4, 5, 6 or 9. You may NOT use your calculator. 

a) 1035

1035 is divisible by 3 because 1 + 0 + 3 + 5 = 9 and 9 is divisible by 3.

1035 is not divisible by 4 because 35 is not divisible by 4. 

1035 is divisible by 5 because it ends on a 5. 

1035 is not divisible by 6 because it is not even, it is divisible by 3 but it needed to meet both criteria.

1035 is divisible by 9 because 1 + 0 + 3 + 5 = 9 and 9 is divisible by 9. 

 

b) 3245510977

3245510977 is not divisible by 3 because 3 + 2 + 4 + 5 + 5 + 1 + 0 + 9 + 7 + 7 = 43 and 43 is not divisible by 3.

3245510977 is not divisible by 4 because 77 is not divisible by 4. 

3245510977 is not divisible by 5 because it doesn't end on a 5 or a 0. 

3245510977 is not divisible by 6 because it is not even and not divisible by 3. 

3245510977 is not divisible by 3 because 3 + 2 + 4 + 5 + 5 + 1 + 0 + 9 + 7 + 7 = 43 and 43 is not divisible by 9.

Exercise 3

a) Why is 12 not a prime number? 

Because you can divide 12 by 1 and by 12 (itself) but you can also divide it by 2, 3, 4 and 6. And you can only divide a prime number by 1 and itself. 

 

b) What is the only even prime number? 

2 is the only even prime number because you can only divide 2 by 1 and by itself. 

 

c) Give all prime numbers less than 30. 

 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

NOTE: 1 is NOT a prime number because dividing 1 by itself and by 1 is exactly the same. So, you only divide it by 1 and therefore 1 can not be divided by 2 numbers. 

 

d) Write 90 as a product of prime numbers. 

90 = 2 x 3 x 3 x 5 

Because: 

90 : 2 = 45 

45 : 3 = 15 

15 : 3 = 5 

5 : 5 = 1 

 

e) Write 72 as a product of prime numbers. 

72 = 2 x 2 x 2 x 3 x 3 

Because: 

72 : 2 = 36 

36 : 2 = 18 

18 : 2 = 9 

9 : 3 = 3 

3 : 3 = 1