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Factors, Multiples and Primes

A 50-minute Grade 4 lesson on finding all the factor pairs of a number, which is also how you find out whether it is prime without guessing.

Factors, Multiples and Primes is a free 50-minute Grade 4 maths lesson plan for Common Core standard 4.OA.B.4 — find factors and multiples, and tell prime from composite numbers. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.

Grade:
Grade 4
Length:
50 minutes
Standard:
4.OA.B.4

Grade 4 · Operations & Algebraic Thinking

4.OA.B.4

Find 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 is prime or composite.

Objective

Students will be able to find all factor pairs of a number to 100 and determine whether it is prime or composite.

Students are successful when they can

  • Finds all factor pairs of a number by testing in order.
  • Knows when to stop testing.
  • Classifies a number as prime or composite and justifies it.

What you need

  • Square tiles for building rectangles
  • Squared paper
  • A hundred square for the sieve activity
  • The printable practice sheet linked at the end of this plan

The lesson

Warm-up — build every rectangle

6 min
  1. Give each pair 12 tiles and ask for every rectangle they can build.
  2. 1 by 12, 2 by 6, 3 by 4. Then give them 13 tiles and let the frustration happen.

Teach — test in order, and know when to stop

15 min
  1. Write the factor pairs of 12 from the rectangles: 1 and 12, 2 and 6, 3 and 4.
  2. Show the system: try 1, then 2, then 3, in order. Nothing gets missed.
  3. Ask when to stop. After 3 comes 4, and 4 is already in a pair we found. Once the two numbers meet, the list is complete.
  4. Do 36 together: 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6. Stop at 6 because it pairs with itself.
  5. Now 13. One and 13, and nothing else. A number with exactly two factors is prime.
  6. Point out that 1 has only one factor, so it is neither prime nor composite. That is a definition, not a trick.
“Test 1, 2, 3, 4 in order and stop when the pair meets in the middle. That is how you know you have found them all, not just the ones you thought of.”

Guided practice — complete the list

14 min
  1. Pairs find all factor pairs for a set of numbers, testing in order and recording where they stopped.
  2. They classify each as prime or composite.
  3. Then they list the first six multiples of a given number and check that number appears as a factor of each.

Independent practice

12 min
  1. Students complete a factors and multiples page.
  2. Incomplete factor lists are the common error and come from unsystematic searching, not from arithmetic.

Close

3 min
  1. Ask whether 51 is prime. Most will say yes.
  2. It is 3 × 17. The systematic test would have caught it, and a guess did not.

What goes wrong, and why

Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.

Says 51 is prime because it is odd and does not look divisible.

Why: Primality is being judged by appearance rather than tested. Odd numbers are often prime, so the heuristic usually works.

Fix: Test 2, 3, 5, 7 in order every time. The system finds 3 × 17 and the guess does not.

Confuses factors with multiples.

Why: Both words describe a relationship between two numbers and are introduced together, so the direction gets lost.

Fix: Factors fit inside; multiples grow outwards. Build the rectangles for factors and count the jumps on a number line for multiples — two different actions.

Says 1 is prime.

Why: It has no factors other than 1 and itself, which sounds like the definition until you notice they are the same number.

Fix: Count the factors. Prime means exactly two different factors; 1 has one. State it as a definition rather than arguing it.

If they are not there yet

  • Build rectangles with tiles for every number rather than dividing. The factor pairs are the rectangles.
  • Work with numbers under 30 where the lists are short and the stopping point comes quickly.

If they finish early

  • Find a number under 50 with exactly six factors.
  • Explain why a square number always has an odd number of factors.
  • Use the sieve of Eratosthenes on a hundred square.

Exit ticket

List all the factor pairs of 24. Is 29 prime? How do you know?

What to look for: 1 and 24, 2 and 12, 3 and 8, 4 and 6. Yes, with the tests up to 5 named. A short factor list means the search was not systematic.

Printable practice for 4.OA.B.4

Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.

Questions about Factors, Multiples and Primes

How long does the Factors, Multiples and Primes lesson take?

50 minutes, split across 5 timed sections: warm-up 6 min, teach 15 min, guided practice 14 min, independent practice 12 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.

Which standard does Factors, Multiples and Primes teach?

CCSS.MATH.CONTENT.4.OA.B.4 — 4.OA.B.4, Operations & Algebraic Thinking for Grade 4: “Find 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 is prime or composite.” In plain terms, find factors and multiples, and tell prime from composite numbers.

What do I need to teach this lesson?

Square tiles for building rectangles, squared paper, a hundred square for the sieve activity and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.

What mistakes should I expect in this lesson?

Three, each a reasoning error rather than carelessness: says 51 is prime because it is odd and does not look divisible; confuses factors with multiples and says 1 is prime. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.

How do I know whether the lesson worked?

The exit ticket asks: “List all the factor pairs of 24. Is 29 prime? How do you know?.” 1 and 24, 2 and 12, 3 and 8, 4 and 6. Yes, with the tests up to 5 named. A short factor list means the search was not systematic. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.

Is there a worksheet to go with Factors, Multiples and Primes?

Yes — 2 printable 4.OA.B.4 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.

Is Factors, Multiples and Primes free to use?

Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 5 September 2026. Please do not resell it or republish it as your own.

Last reviewed 2026-09-05. Aligned to 4.OA.B.4 of the Common Core State Standards for mathematics.