Question

name
class
date
extra practice - factor trees
objective: students will be able to use modeling and visual skills to find the prime factorization of a number.
fill in the missing numbers for each of the factor trees.

(18 factor tree: 18 split into 3 × 6; 6 split into □ × 3; factors: 18: 2 × 3 × 3 = 2 × 3²)
(64 factor tree: 64 split into 8 × 8; 8 split into □ × 4 and 2 × □; 4 split into □ × □; factors: 64: 2 × □ × 2 × □ × □ × □ = 2^□)
(88 factor tree: 88 split into 4 × □; 4 split into □ × 2; □ split into 2 × □; factors: 88: 2 × 2 × 2 × □ = 2³ × 11)

fill in the missing numbers for each of the factor trees.

(60 factor tree 1: 60 split into 6 × □; 6 split into □ × 3; □ split into 2 × □)
(60 factor tree 2: 60 split into □ × □; □ split into 5 × □; □ split into 2 × 3)
factors: 60: 2 × □ × 3 × □ = □² × 3 × □

Explanation:

Step1: Factor 6 into prime factors

$6 = 2 \times 3$

Step2: Factor 8 into prime factors

$8 = 2 \times 4$, $4 = 2 \times 2$

Step3: Factor 88 into prime factors

$88 = 4 \times 22$, $4 = 2 \times 2$, $22 = 2 \times 11$

Step4: Factor 60 (first tree) into primes

$60 = 6 \times 10$, $6 = 2 \times 3$, $10 = 2 \times 5$

Step5: Factor 60 (second tree) into primes

$60 = 10 \times 6$, $6 = 5 \times (2 \times 3)$

Step6: Compile prime factorizations

• $18 = 2 \times 3 \times 3$
• $64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^6$
• $88 = 2 \times 2 \times 2 \times 11 = 2^3 \times 11$
• $60 = 2 \times 2 \times 3 \times 5 = 2^2 \times 3 \times 5$

Answer:

For 18:

• Empty box under 6: $\boldsymbol{2}$

For 64:

• First empty box under left 8: $\boldsymbol{2}$
• Empty box under right 8: $\boldsymbol{4}$
• Empty boxes under 4: $\boldsymbol{2}$, $\boldsymbol{2}$
• Empty box under right 4: $\boldsymbol{2}$
• Prime factorization boxes: $\boldsymbol{2}$, $\boldsymbol{2}$, $\boldsymbol{2}$, $\boldsymbol{2}$; exponent: $\boldsymbol{6}$

For 88:

• Box next to 4: $\boldsymbol{22}$
• Box next to left 2: $\boldsymbol{2}$
• Box next to right 2: $\boldsymbol{11}$
• Prime factorization box: $\boldsymbol{11}$

For first 60 tree:

• Box next to 6: $\boldsymbol{10}$
• Box next to 3: $\boldsymbol{2}$
• Box next to 2: $\boldsymbol{5}$

For second 60 tree:

• Boxes at top: $\boldsymbol{10}$, $\boldsymbol{6}$
• Box next to 5: $\boldsymbol{6}$

60 prime factorization boxes:

$\boldsymbol{2}$, $\boldsymbol{5}$, $\boldsymbol{2}$, $\boldsymbol{5}$