SSAT Upper Level Quantitative Flashcards: Prime And Composite Numbers

What this deck covers

This deck focuses on Prime And Composite Numbers, giving you a quick way to review the definitions, rules, and examples that matter most for SSAT Upper Level Quantitative.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Identify whether $61$ is prime or composite.

Answer: $61$ is prime. No divisibility by primes up to $\sqrt{61} \approx 7.8$ (2, 3, 5, 7).

Flashcard 2: Identify whether $21$ is prime or composite.

Answer: $21$ is composite. Factors as $3 \times 7$, showing more than two positive divisors.

Flashcard 3: Identify whether $53$ is prime or composite.

Answer: $53$ is prime. No divisibility by primes up to $\sqrt{53} \approx 7.3$ (2, 3, 5, 7).

Flashcard 4: Identify whether $97$ is prime or composite.

Answer: $97$ is prime. No divisibility by primes up to $\sqrt{97} \approx 9.8$ (2, 3, 5, 7).

Flashcard 5: Identify whether $35$ is prime or composite.

Answer: $35$ is composite. Factors as $5 \times 7$, indicating multiple divisors.

Flashcard 6: What is the key stopping point when testing whether $n$ is prime by trial division?

Answer: Test primes up to and including $\sqrt{n}$. Any factor larger than $\sqrt{n}$ pairs with one smaller, so checking up to this suffices.

Flashcard 7: What is the definition of a prime number in terms of its positive divisors?

Answer: A number $>1$ with exactly two positive divisors: $1$ and itself. This criterion ensures the number cannot be expressed as a product of two integers greater than 1.

Flashcard 8: What is the definition of a composite number in terms of its positive divisors?

Answer: A number $>1$ with more than two positive divisors. Such numbers can be factored into products of smaller integers greater than 1.

Flashcard 9: Which statement is true: If $n$ is composite, then it has a prime factor $\le \sqrt{n}$?

Answer: True: every composite $n$ has a prime factor $\le \sqrt{n}$. The smallest prime factor of a composite must not exceed its square root.

Flashcard 10: Identify whether $77$ is prime or composite.

Answer: $77$ is composite. Factors as $7 \times 11$, showing it is not prime.

Flashcard 11: Identify whether $29$ is prime or composite.

Answer: $29$ is prime. No divisibility by primes up to $\sqrt{29} \approx 5.4$ (2, 3, 5).

Flashcard 12: Identify whether $51$ is prime or composite.

Answer: $51$ is composite. Factors as $3 \times 17$, with more than two divisors.

Flashcard 13: Identify whether $17$ is prime or composite.

Answer: $17$ is prime. No divisibility by primes up to $\sqrt{17} \approx 4.1$ (i.e., 2 or 3).

Flashcard 14: Which number is the only even prime number?

Answer: $2$. All even numbers greater than this are divisible by it and thus composite.

Flashcard 15: What is the correct classification of $1$: prime, composite, or neither?

Answer: $1$ is neither prime nor composite. It has only one positive divisor, failing the criteria for both prime and composite.

Flashcard 16: Identify whether $49$ is prime or composite.

Answer: $49$ is composite. Factors as $7 \times 7$, proving it is not prime.

Flashcard 17: What is the correct classification of $2$: prime or composite?

Answer: $2$ is prime. Its only positive divisors are 1 and itself, meeting the prime definition despite being even.

Flashcard 18: What is the divisibility rule that shows a number ending in $0$ or $5$ is composite (if $>5$)?

Answer: If last digit is $0$ or $5$, then $5\mid n$ so composite for $n>5$. Ending in 0 or 5 indicates divisibility by 5, confirming factors other than 1 and $n$.

Flashcard 19: Identify whether $121$ is prime or composite.

Answer: $121$ is composite. Factors as $11 \times 11$, indicating composite nature.

Flashcard 20: Identify whether $37$ is prime or composite.

Answer: $37$ is prime. No divisibility by primes up to $\sqrt{37} \approx 6.1$ (2, 3, 5).

Flashcard 21: What divisibility test proves an integer is composite if the sum of its digits is divisible by $3$?

Answer: If $3\mid$ (digit sum), then $3\mid n$ so $n$ is composite. Divisibility by 3 for $n>3$ implies additional factors beyond 1 and itself.

Flashcard 22: Identify whether $57$ is prime or composite.

Answer: $57$ is composite. Factors as $3 \times 19$, confirming composite status.

Flashcard 23: Identify whether $91$ is prime or composite.

Answer: $91$ is composite. Factors as $7 \times 13$, with multiple divisors.

Flashcard 24: What quick test proves an integer $n>2$ is composite if it is even?

Answer: If $2\mid n$, then $n$ is composite. Even divisibility by 2 for $n>2$ means it has divisors other than 1 and itself.

Flashcard 25: Identify whether $59$ is prime or composite.

Answer: $59$ is prime. No divisibility by primes up to $\sqrt{59} \approx 7.7$ (2, 3, 5, 7).