Mystery Number Factor Riddles

4th Grade MathFactors and Multiples4 pages

About this worksheet

Factor and multiple work for 4th grade on Common Core 4.OA.4. Two scaffolded boxes walk students through every factor pair of 24 and 36, with the pair equations started (1 ร— ______ = 24) and a line for the full factor list. A sort splits 7, 12, 19, 21, 29, 35, 41 and 48 into prime and composite columns, four yes-or-no items check whether numbers like 54 and 45 are multiples of 6 and 7, and two mystery-number riddles combine the clues: a multiple of both 4 and 6 between 20 and 30, and an odd prime under 20 whose digits sum to 8. The key resolves both riddles.

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Curriculum objectives covered

4.OA.4

โ€œFind all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.โ€

Each part hits one clause: factor pairs for 24 and 36, the prime-composite sort, the four multiple checks, and riddles that need all three ideas at once.

What's inside this worksheet

Part 1: Factor Pairs

The 24 box scaffolds four pair equations and the 36 box five, each ending with the factors listed least to greatest.

Part 2: Prime or Composite?

Definitions are printed, then eight numbers (7, 12, 19, 21, 29, 35, 41 and 48) sort into two columns.

Part 3: Multiples Detective

Is 54 a multiple of 6? Is 45 a multiple of 7, 72 of 8, 63 of 9? Each wants Yes or No plus the thinking shown.

Part 4: Math Mystery Clues

Mystery Number A lives between 20 and 30 and is a multiple of 4 and of 6. Mystery Number B is odd, under 20, has exactly two factors, and its digits sum to 8.

How teachers use it

Riddles as the hook

Read Mystery Number A aloud before passing anything out. Working backwards into Parts 1 to 3 for the tools beats working forward.

Show the near-miss

In Part 3, question 2 is the only No. Ask students to prove it by finding the multiples of 7 on either side of 45.

Factor rainbow check

Have students draw arcs pairing the factors they listed for 36. The unpaired 6 in the middle is the square-number conversation.

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