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e How many siblings do you expect Anson has?

10 Are the following statements true or false?

a A multiple of a particular number is always smaller than that number.

b 2 is a factor of every even number c 3 is a factor of every odd number. d A factor is always greater than or equal to the given number. e When considering a particular number, that number is both a factor and a multiple of itself. a What is the smallest number that has 1, 2, 3, 4, 5, 6, 7 and 8 as factors? b What is the smallest number that has 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 as factors? b What are the factors of 100?

11 60 is a number with many factors. It has a total of 12 factors and, interestingly, it has each of the numbers 1, 2, 3, 4, 5, 6 as a factor.

12 a What numbers can claim that the number 100 is a multiple of them? (For example, 5 could claim that 100 is a multiple of it.)

13 All Australian AM radio stations have frequencies that are multiples of 9. For example, a particular radio station has a frequency of 774 (kilohertz or kHz). Find three other AM radio stations and show their frequencies are, indeed, multiples of 9

14 A particular number is a multiple of 6 and also a multiple of 15. This tells you that 6 and 15 are factors of the number. List all the other numbers that must be factors.

ENRICHMENT: Factors and multiples with spreadsheets

15 a Design a spreadsheet that will enable a user to enter any number between 1 and 100 and it will automatically list the first 30 multiples of that number.

b Design a spreadsheet that will enable a user to enter any particular number between 1 and 100 and it will automatically list the number’s factors.

c Improve your factor program so that it finds the sum of the factors and also states the total number of factors for the particular number d Use your spreadsheet program to help you find a pair of amicable numbers. A pair of numbers is said to be amicable if the sum of the factors for each number, excluding the number itself, is equal to the other number. Each number that makes up the first such pair of amicable numbers falls between 200 and 300.

An example of a non-amicable pair of numbers:

12 : factor sum = 1 + 2 + 3 + 4 + 6 = 16

16 : factor sum = 1 + 2 + 4 + 8 = 15

The factor sum for 16 would need to be 12 for the pair to be amicable numbers.

Helpful Microsoft Excel formulas

INT(number) – Rounds a number down to the nearest integer (whole number).

MOD(number, divisor) – Returns the remainder after a number is divided by the divisor.