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Advanced Factors Challenge

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Advanced Factors Challenge

Choose the best answer for each question. For questions that ask you to explain or show your working, write your thinking clearly.

Factor Detective

Select the correct answer. For the factor-pair question, select every correct option.

1.Which number is not a factor of 56?

2.How many positive factors does 30 have?

3.Which sentence correctly describes a prime number?

It has exactly one factor.
It has exactly two positive factors.
It is always an even number.
It has more than four factors.

4.Which options are factor pairs of 36? Select all that apply.

1 × 36
2 × 18
3 × 10
4 × 9
6 × 6

Factor Analysis and Problem Solving

Show your working where asked.

5.Draw a factor tree for 84 and continue until every branch ends in a prime number.

6.Talia says every even whole number has 2 as a factor. Is Talia right? Explain why and give two examples.

7.Find a whole number greater than 20 and less than 30 that has exactly six positive factors. Write the number and list all six factors.

8.A display has 45 counters arranged in 5 equal rows. How many counters are in each row? Write a division sentence to show how you know.

Extension and Creative Thinking

Use factors to explain your ideas.

9.Write two different whole numbers that each have exactly four positive factors. Explain how you can check the factor count for each number.

10.A baker has 48 muffins and wants to place them in equal rows with none left over. Give three different row-by-column arrangements. Which arrangement would you choose for a wide display, and why?

11.Compare the positive factors of 16 and 24. List the factors of each number, then identify their common factors.