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Factors and Multiples Exploration

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Factors and Multiples Exploration

A community pop-up market is packing supplies into equal groups. Use factors, multiples and prime factorisation to solve each challenge. Show working where you can. All numbers are whole numbers greater than zero.

Pack it fairly

The market has 36 juice boxes to pack into identical crates, with none left over.

1.Which number is a factor of 36?

2.List every positive factor of 36 in ascending order.

3.The organisers want to make crates with 4 juice boxes in each. How many full crates can they make? Explain why 4 works.

Find the shared schedules

A food stall restocks every 8 minutes. A drinks stall restocks every 12 minutes. They both restock at 9:00 am.

4.Write the first five positive multiples of 8 and the first five positive multiples of 12. Identify the first common multiple.

5.How many minutes after 9:00 am will the two stalls next restock together? What time will it be?

Investigate and explain

Use the number grid to help check which numbers are prime. A prime number has exactly two positive factors: 1 and itself.

6.Write all the prime numbers from 1 to 30.

7.A volunteer says, “1 is prime because it divides into itself.” Is the volunteer correct? Explain using the definition of a prime number.

8.Write 84 as a product of prime factors. Show the factorisation using index notation.

9.Two stalls have 24 savoury pies and 30 fruit pies. They want to make the greatest possible number of identical mixed platters, using every pie. How many platters can they make, and what goes on each platter?

10.Explain the difference between a factor and a multiple. Use 6 and 30 in your explanation.