Prime Factorization: Homework

Prime or composite, factor trees, dividing by the least prime, and exponents.

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Part A — Prime or Composite? / 5

Type prime or composite.

Write the prime factors from least to greatest, with commas between. You can use a factor tree or divide by the least prime.

Each problem has a mistake in it.

1.
A student writes 2 × 3 × 6 for the prime factorization of 36. Which number should be split again?Answer
2.
A student says 1 is the smallest prime. What is the smallest prime?Answer
3.
A student says 2 is not prime because it is even. Is 2 prime? Type yes or no.Answer
4.
Two students factor 48. One writes 2 × 24, then 2 × 2 × 12 and keeps going. The other writes 6 × 8 and keeps going. Will they end with the same primes? Explain.Answer

These numbers are real. Break each one into primes.

Write your answer in a sentence or two.

1.
Chairs are set out in equal rows. Explain why 31 chairs can only be set out in one row, and why 32 chairs can be set out in several ways.Answer
2.
Write 360 as a product of primes with exponents, and check it by multiplying.Answer

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Total / 20

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Notes

Part A — prime or composite.

Part B — the prime factors.

Part C — the answers.

6. It is not prime.
2
Yes. 2 has exactly two factors, 1 and 2, and it is the only even prime.
Answers vary. Yes. Every composite number has exactly one prime factorization, ignoring order, so both end with 2 × 2 × 2 × 2 × 3.

Part D — the prime factors.

Part E — one correct answer, and what a good explanation says.

Answers vary. 31 is prime, so its only factors are 1 and 31. 32 is composite, so it has more factors, such as 2 and 16 or 4 and 8.
Answers vary. 360 = 2 × 2 × 2 × 3 × 3 × 5, which is 2³ × 3² × 5. Check: 8 × 9 × 5 = 360.