Fractions
Prime factor trees
Break composite numbers into factor pairs until every branch ends in a prime, retaining repeated factors.
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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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Write each number as a product of prime factors in increasing order. Repeat a prime as many times as needed for the product to equal the original number.
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Learning objective
What this activity builds
Decompose each number into prime factors and verify the complete product by multiplication.
Worked example
Write 84 as a product of prime factors.
84 = 2 × 2 × 3 × 7
Divide 84 by 2 to get 42, divide 42 by 2 to get 21, then split 21 into 3 × 7. All four factors are prime and their product is 84.
Teaching notes
Make the practice count
- If a remaining factor is composite, keep splitting it. Reaching a smaller number is not enough; every final factor must be prime.
- Use a multiplication sign between factors. A list of prime values alone does not show the requested product.
- The answer key writes repeated factors explicitly. Once learners understand the product, discuss how exponents can abbreviate repetitions.
- Different valid first splits can produce the same prime factorization. Compare the final factors, not the shape of the working.
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