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Factor Pairs Exploration

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Factor Pairs Exploration

A market stall is packing produce into equal rows. A factor pair tells how many rows and how many items are in each row: rows × items per row = total. Find every possible rectangular arrangement, then use factor pairs to solve the stall’s challenges.

Explore the arrangements

Factor pairs can be shown as rectangles. Each dot is one item; the rows and columns show a multiplication fact.

1.The stall has 24 apples. List all factor pairs of 24, writing each pair once with the smaller factor first.

2.For a crate of 36 feijoas, which option is not a possible equal-row arrangement? Choose one and explain how you know.

3 rows of 12
4 rows of 9
5 rows of 7
6 rows of 6

3.A tray holds 40 kūmara in equal rows. List all factor pairs of 40, with the smaller number first.

Use factors to solve stall puzzles

Check each arrangement with multiplication. Remember, a square arrangement such as 6 rows of 6 is still a factor pair.

4.A box has 48 apples. Complete the matching multiplication and division facts for the factor pair (6, 8): 6 × 8 = __; 48 ÷ 6 = __; 48 ÷ 8 = __.

5.True or false? The pair (7, 7) is a factor pair of 49. Write the multiplication fact that proves your answer.

TrueFalse

6.The stall has 30 lemons. Select every number that is a factor of 30.

7.A fruit display uses 32 mandarins. Aria says there are exactly three factor pairs. Is Aria correct? List all the factor pairs to support your answer.

8.A stall has 54 carrots to pack. Name two different equal-row arrangements and write a multiplication fact for each.

9.The stall has 36 apples and 24 pears. Each fruit type must be put into rows with the same number of items per row, and no fruit can be left over. What is the greatest number of items per row that works for both fruit types? Show how you checked.

10.Choose one factor pair for 60 and explain how it proves that 60 items can be packed into equal rows. Use the words factor and product.