6.NOS.4 Lesson 6-13-part2 Apply Day · Set B
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6.13 · Part II

Second Practice Form · Independent Application and Spiral Review

Prime Factorization · Prime number

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■ ADVANCED CONCEPT ANCHOR: 6.13 · Part II
1Prime Factorization & Factor Trees
2The Structural Procedure
  1. Prime Number: Has exactly two factors (1 and itself, e.g. 2, 3, 5, 7, 11)
  2. Split composite number into factor pairs until every branch ends in a prime
  3. Write final product using exponents in ascending order (e.g. 60 = 2² × 3 × 5)
3Mathematical Word Bank
  • Prime Factorization (Factorización prima) — Writing a whole number as a product of only prime numbers.
  • Prime number (Número primo) — A number bigger than 1 that you can only divide by 1 and itself.
  • Composite number (Número compuesto) — A number bigger than 1 that you can divide by more than just 1 and itself.
  • Factor (Factor) — A factor of a whole number divides it evenly, with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4.
  • Factor tree (Árbol de factores) — A picture that splits a number into its prime numbers, step by step.
  • Exponent (Exponente) — A small number that tells how many times to multiply a number by itself.
4Watch out
  • A common mistake in Prime Factorization is stopping the factor tree too soon — leaving a composite number like 4, 6, 8, or 9 in the final answer instead of continuing to split it. For example, writing 20 = 4 × 5 as the prime factorization (4 is composite) instead of finishing with 20 = 2 × 2 × 5. Before you submit, check every number in your final answer: if any factor can still be broken into smaller factors, the tree isn't finished yet.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 GUIDED FILL
    66

    Build a new factor tree for 66. Write the prime factorization.

    1. 1The smallest prime factor of 66 is ___.
    2. 266 ÷ 2 = ___.
    3. 3Keep splitting until every end number is prime. Write the prime factorization: ___.
    Final answer:
  2. 2 GUIDED FILL
    70

    Build a new factor tree for 70. Write the prime factorization.

    1. 1The smallest prime factor of 70 is ___.
    2. 270 ÷ 2 = ___.
    3. 3Keep splitting until every end number is prime. Write the prime factorization: ___.
    Final answer:
  3. 3 MULTIPLE CHOICE
    Factor Tree for 78
    7862313

    The final lock asks for the prime factorization of 78 written as a product of primes. Which is correct?

    1. A2 × 3 × 13
    2. B2 × 39
    3. C3 × 26
    4. D6 × 13
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Which of the following is a prime number?

    1. A17
    2. B15
    3. C21
    4. D9
    ✏️ Workspace & Solution Steps
  5. 5 MULTIPLE CHOICE

    What is the prime factorization of 30?

    1. A2 × 3 × 5
    2. B5 × 6
    3. C2 × 15
    4. D3 × 10
    ✏️ Workspace & Solution Steps
  6. 6 MULTIPLE CHOICE

    What is the prime factorization of 18?

    1. A2 × 3 × 3
    2. B2 × 9
    3. C3 × 6
    4. D6 × 3
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 7 OPEN RESPONSE

    Choose any two-digit composite number. Show TWO different factor trees that both lead to the same prime factorization. Explain why every composite number has only one prime factorization.

    ✏️ Mathematical Justification & Response
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It