alleryWhich of the following numbers is prime?
- 61
- 63
- 51
- 57
Show answer and solution
Correct answer: A. 61
61 has no divisors other than 1 and itself.
51 = 3·17, 57 = 3·19, 63 = 7·9. So 61 is the prime.
GRE Real Numbers and Polynomials — practice questions — page 3
Explore 73 free Real Numbers and Polynomials questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 61–73 of 73.
Which of the following numbers is prime?Read the answer and worked solution →The prime factorisation of 360 is:Read the answer and worked solution →The Fundamental Theorem of Arithmetic guarantees that:Read the answer and worked solution →Find the HCF of 24 and 36.Read the answer and worked solution →Find the LCM of 12 and 18.Read the answer and worked solution →If HCF(a, b) = 9 and a · b = 1620, find LCM(a, b).Read the answer and worked solution →Two bells ring at intervals of 9 and 15 minutes. They ring together at noon. When do they ring together again?Read the answer and worked solution →Which of the following is an irrational number?Read the answer and worked solution →Will the decimal expansion of 13/125 terminate?Read the answer and worked solution →The decimal expansion of 1/6 is:Read the answer and worked solution →Which of the following will have a terminating decimal expansion?Read the answer and worked solution →Numbers that fill the number line completely (every point on the line corresponds to such a number) are called:Read the answer and worked solution →If p is prime and p divides a², then p divides a. This step is used to prove which number irrational in your syllabus?Read the answer and worked solution →
Worked practice questions
The prime factorisation of 360 is:
- 2² × 3² × 5²
- 2³ × 3² × 5
- 2² × 3³ × 5
- 2³ × 3 × 5²
Show answer and solution
Correct answer: B. 2³ × 3² × 5
We have 360 = 8 × 45.
That is 360 = 2³ × 9 × 5.
So 360 = 2³ × 3² × 5.
The Fundamental Theorem of Arithmetic guarantees that:
- no two primes are equal
- primes are infinite
- composites factor uniquely
- all integers are prime
Show answer and solution
Correct answer: C. composites factor uniquely
The theorem says: every composite number factorises into primes, and that factorisation is unique up to the order of the factors.
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