Factors
Prime factorization
Express composite numbers as products of primes, retaining repeated factors. Print 10, 15 or 20 questions for ranges up to 50, 81, 144 or 200.
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List distinct prime factors
Identify the different prime divisors of each composite number. List each prime once, using selectable ranges through 200 and a separate key.
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Write the prime factors of each number in increasing order, using each prime only once. Do not include 1 or composite factors.
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Learning objective
What this activity builds
Distinguish a prime divisor from a composite factor and recognize when repeated primes count as one distinct value.
Worked example
Which different prime factors divide 72?
2, 3
72 = 2 × 2 × 2 × 3 × 3. Only two different primes occur. Although 6 also divides 72, it is composite and does not belong in this list.
Teaching notes
Make the practice count
- Use a factor tree when the prime divisors are not immediately clear, then remove repeated values from the final list.
- Check each listed number twice: it must divide the original number exactly, and it must itself be prime.
- A power of a prime, such as 64, has only one distinct prime factor even though that factor appears many times in its decomposition.
- Keep the wording explicit. This worksheet asks for different prime factors, while the separate factorization worksheet asks for their complete product.
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Break composite numbers into factor pairs until every branch ends in a prime, retaining repeated factors.
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