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Place value and number senseGrade 4

Prime and composite numbers worksheet

Each line shows a number and a blank for prime or composite. Choose a limit of 30, 50, 100 or 200, turn on the factor list for extra proof, and print with an answer key or save a PDF.

By Paul Gunder. Free to print for home, classroom and office use; see how our printables are made.

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Prime and Composite Numbers to 1002 pages, answer key from page 2 · US Letter

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NameDateScorePrime and Composite Numbers to 100Write prime or composite next to each number. A prime number has exactly two factors: 1 and itself.1.13 2.75 3.7 4.50 5.81 6.67 7.87 8.60 9.32 10.78 11.31 12.66 13.45 14.54 15.89 16.93 17.12 18.51 19.91 20.33 21.56 22.42 23.72 24.5 25.71 26.2 27.22 28.95 29.10 30.82 PrintablePal.com · free printablesPrime and Composite Numbers to 100
Worksheet, page 1
Prime and Composite Numbers to 100: answer key1.13 prime2.75 composite3.7 prime4.50 composite5.81 composite6.67 prime7.87 composite8.60 composite9.32 composite10.78 composite11.31 prime12.66 composite13.45 composite14.54 composite15.89 prime16.93 composite17.12 composite18.51 composite19.91 composite20.33 composite21.56 composite22.42 composite23.72 composite24.5 prime25.71 prime26.2 prime27.22 composite28.95 composite29.10 composite30.82 compositePrintablePal.com · free printablesAnswer key
Answer key, page 1

On this page

Two kinds of numbers

A prime number has exactly two factors, 1 and itself. A composite number has more than two. Fourth graders learn to sort numbers within 100 into these two groups, and the sorting depends on knowing factors and being quick with multiplication facts. The number 1 is neither prime nor composite, so the sheet never prints it: every number runs from 2 up to the chosen limit.

The page header repeats the definition of a prime, which is helpful because many students mix up the words. A memory aid: composite numbers are "composed" of smaller factors.

Settings and how to use them

  • Numbers up to. Choose 30, 50, 100 or 200. At 30 the primes are few and recognizable (2, 3, 5, 7, 11, 13, 17, 19, 23, 29). At 100, students must test numbers such as 91, which looks prime and is not. At 200 the sheet becomes a stretch for strong students.
  • Also list the factors. Off by default. With it on, each line has a second blank for every factor in order, and the layout changes from three columns to one. This setting makes the sheet slower but turns a guess into a proof, because a student cannot call 51 prime if they have to write down 3 and 17.
  • Number of problems. From 12 to 40.

Start with 30 and no factors, then increase the limit, and use the factor version when you suspect students are guessing from how a number looks. It is also a solid way to review factor pairs before moving on to fractions.

Worked example: 51 and 53

Is 51 prime?

  1. Start with the quick divisibility checks. It is odd, so 2 is out. It does not end in 0 or 5, so 5 is out.
  2. Add the digits: 5 + 1 = 6, and 6 is a multiple of 3, so 51 is divisible by 3.
  3. Divide: 51 ÷ 3 = 17, so 51 = 3 × 17.
  4. A number with a factor other than 1 and itself is composite. With the factor option on, the key lists 1, 3, 17, 51.

Is 53 prime?

  1. It is odd, and it does not end in 0 or 5.
  2. The digit sum is 8, so it is not divisible by 3.
  3. Try 7: 7 × 7 = 49 and 7 × 8 = 56, so 7 does not divide 53.
  4. The next candidate, 11, is already too big, since 11 × 11 = 121 is above 53. Testing stops once the divisor squared passes the number.
  5. So 53 is prime, and its only factors are 1 and 53.

Where students slip

  • Calling 2 composite, or 9 prime. 2 is the only even prime. Odd numbers like 9, 15 and 21 are composite, so oddness alone is not proof.
  • Trusting appearances. Numbers such as 51, 57, 87 and 91 look prime but are not. The answer key with factors shows the hidden pair: 91 = 7 × 13.
  • Incomplete factor lists. For 36, the full list is 1, 2, 3, 4, 6, 9, 12, 18, 36, but a student may stop at 1, 2, 3, 4, 6 and forget the larger half of each pair. Teach them to write factors in pairs from the outside in.
  • Counting 1. Remind students that 1 has only one factor, so it is not prime.

Factor thinking is the same skill used in simplifying fractions, so those pages pair well with this one. For strengthening fact recall, use the times tables up to 12. Students who like number puzzles might also enjoy the fact family worksheets.

Sources

  1. Common Core State Standards: Grade 4 Operations and Algebraic Thinking (4.OA.B.4, factors, multiples, prime and composite) thecorestandards.org