Find the Rule Practice Test Worksheets
Build confidence with printable Find the Rule worksheets and focused number reasoning practice tests. Students learn to test factors, multiples, primes, powers, digit properties, and number patterns while improving accuracy with logical elimination questions.
For students who can calculate fluently, but need practice proving which rule fits every number in a set.
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The Rules Every Find the Rule Question Uses
Each question gives 3 or 4 numbers and five possible rules. The correct option must be true for every number, so students need to test the whole set rather than stop after the first match.
Rule 1: Even products stay even
When an even number is multiplied by any whole number, the result is always even.
Example: 6 × 5 = 30 and 8 × 7 = 56, so both products are even even though one multiplier is odd.
Rule 2: Separate factors from multiples
Factor rules say a number divides into a target. Multiple rules say the number is made by multiplying.
Example: 6, 8, and 36 are all factors of 72 because 72 divides by each one exactly.
Rule 3: Check power and shape numbers
Some sets use square numbers, cube numbers, triangular numbers, or numbers just beside them.
Example: 8, 27, 125, and 729 are cube numbers: 2 cubed, 3 cubed, 5 cubed, and 9 cubed.
Rule 4: Use digit tests carefully
Digit-sum, palindrome, and tens-units rules can look convincing, but one counterexample is enough.
Example: 484, 676, 707, and 808 are palindromes because each reads the same forwards and backwards.
3 Worked Find the Rule Examples
Each example checks every option, just like the answer keys in the printable tests.
Which rule fits 18, 108, 153, and 180?
Options:
A) Their tens digit is greater than their units digit.
B) They are all multiples of 9.
C) They are all three-digit numbers.
D) They are all even numbers.
E) They are all multiples of 4.
Worked Method
Check A: 18 and 108 do not have a tens digit greater than their units digit, so A fails.
Check B: 18 ÷ 9 = 2, 108 ÷ 9 = 12, 153 ÷ 9 = 17, and 180 ÷ 9 = 20. All four work.
Check C: 18 is a two-digit number, so C fails.
Check D: 153 is odd, so D fails.
Check E: 18 and 153 are not multiples of 4, so E fails.
Answer: B, they are all multiples of 9.
Tip: Do not stop when one option sounds plausible. A single counterexample eliminates a rule.
Which rule fits 3, 20, and 120?
Options:
A) They are all factors of 60.
B) They are all factors of 120.
C) They are all multiples of 12.
D) They are all multiples of 5.
E) They are all 1 less than a square number.
Worked Method
Check A: 120 is not a factor of 60, so A fails.
Check B: 120 ÷ 3 = 40, 120 ÷ 20 = 6, and 120 ÷ 120 = 1. All three are factors of 120.
Check C: 3 and 20 are not multiples of 12, so C fails.
Check D: 3 is not a multiple of 5, so D fails.
Check E: 20 is not 1 less than a square number, so E fails.
Answer: B, they are all factors of 120.
Tip: Factor rules feel backwards: the set numbers must divide exactly into the target number.
Which rule fits 16, 66, and 121?
Options:
A) They are all 1 more than a multiple of 5.
B) They are all multiples of 6.
C) They are all even numbers.
D) They are all palindromic numbers.
E) They are all square numbers.
Worked Method
Check A: Subtract 1 from each number: 15, 65, and 120. These are all multiples of 5, so A works.
Check B: 16 and 121 are not multiples of 6, so B fails.
Check C: 121 is odd, so C fails.
Check D: 16 is not a palindromic number, so D fails.
Check E: 66 is not a square number, so E fails.
Answer: A, they are all 1 more than a multiple of 5.
Tip: Hidden rules often use one step before the familiar property, such as subtracting 1 before checking multiples.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Find the Rule pack contains 90 multiple-choice questions across 3 printable test sets. Students practise factors, multiples, primes, powers, digit properties, pattern recognition, and logical elimination.
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