which of these numbers is prime?

choose 1 answer:

a 15
b 45
c 63
d 73
e 88

Question

which of these numbers is prime?

choose 1 answer:

a 15
b 45
c 63
d 73
e 88

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Prime Numbers", "Composite Numbers", "Factors and Multiples" ], "new_concepts": [], "current_concepts": [ "Prime Numbers", "Composite Numbers", "Factors and Multiples" ] } ## Define prime and composite numbers Using the *Prime Numbers* and *Composite Numbers* knowledge points $$ \begin{aligned} &\text{Prime: exactly two distinct positive divisors (1 and itself).}\ &\text{Composite: more than two distinct positive divisors.} \end{aligned} $$ ## Analyze options 15, 45, and 63 Using the *Factors and Multiples* knowledge point $$ \begin{aligned} &15 = 3 \times 5 \implies \text{divisors: } 1, 3, 5, 15 \quad (\text{composite})\ &45 = 9 \times 5 \implies \text{divisors: } 1, 3, 5, 9, 15, 45 \quad (\text{composite})\ &63 = 9 \times 7 \implies \text{divisors: } 1, 3, 7, 9, 21, 63 \quad (\text{composite}) \end{aligned} $$ ## Analyze options 73 and 88 Using the *Factors and Multiples* and *Prime Numbers* knowledge points $$ \begin{aligned} &88 = 8 \times 11 \implies \text{divisors: } 1, 2, 4, 8, 11, 22, 44, 88 \quad (\text{composite})\ &\sqrt{73} \approx 8.54 \implies \text{test primes: } 2, 3, 5, 7\ &73 \pmod 2 e 0, \quad 73 \pmod 3 e 0, \quad 73 \pmod 5 e 0, \quad 73 \pmod 7 e 0\ &\text{Thus, } 73 \text{ is prime.} \end{aligned} $$

(A) 15

(B) 45

(C) 63

(D) 73

(E) 88

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Number Theory", "Prime Numbers" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Define prime and composite numbers

Analyze options 15, 45, and 63

Analyze options 73 and 88

Answer: