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Classify Numbers as Prime or Composite

Students determine whether a whole number from 1 to 100 is prime (exactly two factors: 1 and itself) or composite (more than two factors). They use factor pairs to justify their classifications and learn that 1 is neither prime nor composite.

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Classify Numbers as Prime or Composite

Grade 4 · Factors, Multiples, Primes, and Composites · question 1 of 3

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20 rungs. A star at the top.

Which of these numbers is prime: 3, 4, 9 or 15?

How it is taught

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A prime number has exactly two factors.

Those factors are 1 and the number itself.

A composite number has more than two factors.

Read it: Test the numbers in order

Which pairs of numbers multiply to make 24? Test 1, 2, 3 and on: 1 × 24, 2 × 12, 3 × 8, 4 × 6. At 6 the pair is one already found.

  1. Start at 1 and test each number in order.
  2. If it divides with no remainder, write the pair it makes.
  3. Stop when the next pair would be one you have already found.

Every factor pair has one number that is the smaller of the two, so testing in order finds each pair once.

A number with only the pair 1 and itself is prime; any other pair makes it composite.

1 has only one factor, so it is neither prime nor composite.

Each number that divides with no remainder makes a factor pair.

Calling 9 prime because it is odd.

9 = 3 × 3 is another factor pair, so 9 is composite. Odd numbers can be composite too.

What is the smallest factor of 91 that is more than 1? — 7. 91 ÷ 7 = 13, so 91 is composite, though it is odd.

Is 12 prime or composite?

Let's classify numbers as prime or composite. We'll test the number twelve.

A prime number has exactly two factors: one and itself.

A composite number has more than two factors.

Let's find every factor pair of twelve.

One times twelve equals twelve. That's our first pair.

Two times six equals twelve. Another pair!

Three times four equals twelve. A third pair!

Let's list all the factors: one, two, three, four, six, and twelve. That's six factors.

Six factors is way more than two.

So twelve is composite. Great work!

Is 12 prime or composite?12Prime or Composite?PRIME:exactly 2 factors (1 and itself)COMPOSITE:more than 2 factorsFactor pairs of 12:1 × 12 = 122 × 6 = 123 × 4 = 12Factors: 1, 2, 3, 4, 6, 12→ 6 factors total6 factors > 2 factors12 is COMPOSITEANSWERComposite6 factors
Grade 4 · Using factor pairs to classify

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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