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Example 2

Listing multiples

Write down the first six multiples for each of these numbers.

a 11 b 35

SOLUTION a 11, 22, 33, 44, 55, 66

EXPLANATION b 35, 70, 105, 140, 175, 210

The first multiple is always the given number. Add on the given number to find the next multiple. Repeat this process to get more multiples.

Now you try

Start at 35, the given number, and repeatedly add 35 to continue producing multiples.

Write down the first six multiples for each of these numbers.

a 4 b 26

Example 3

Finding factor pairs

Express 195 as a product of two factors, both of which are greater than 10.

SOLUTION

195 = 13 × 15

Now you try

Exercise 2A

FLUENCY

EXPLANATION

Systematically divide 195 by numbers greater than 10 in an attempt to find a large factor. The number 13 goes into 195 a total of 15 times with no remainder 19 6 5 015 13 a 12 b 48 a 10 d 36 b 24 c 17 e 60 f 42 g 80 h 29 i 28

1 Find the complete set of factors for each of these numbers.

2 List the complete set of factors for each of the following numbers.

3 Write down the first six multiples for each of the following numbers.

4 Fill in the gaps to complete the set of factors for each of the following numbers.

5 Which number is the incorrect multiple for each of the following a Which number has the most factors? b Which number has the fewest factors? c Which numbers have an odd number of factors?

6 Consider the set of whole numbers from 1 to 25 inclusive.

7 Express each of the following numbers as a product of two factors, both of which are greater than 10 a How long do they run for? b How many laps did Zane run? c How many laps did Matt run? a How many lollies does Anson put in each of his friends’ lolly bags? b How many lollies does Anson have left over to eat himself? c How many lollies will now go into each of the 13 lolly bags? d What are the different possible number of sibling(s) that Anson could have?

8 Zane and Matt are both keen runners. Zane takes 4 minutes to jog around a running track and Matt takes 5 minutes. They start at the same time and keep running until they both cross the finish line at the same time.

9 Anson has invited 12 friends to his birthday party. He is making each of them a ‘lolly bag’ to take home after the party. To be fair, he wants to make sure that each friend has the same number of lollies. Anson has a total of 300 lollies to share among the lolly bags.

Anson then decides that he wants a lolly bag for himself also.

After much pleading from his siblings, Anson prepares lolly bags for them also. His sister Monique notices that the total number of lolly bags is now a factor of the total number of lollies.