MATHS 5 Marks Questions

(a) True.
A prime number must end in 1, 3, 7, or 9 (except for the number 2) because any number ending in 0, 2, 4, 6 or 8 is divisible by 2.
Thus, there is no prime number whose units digit is 4.
(b) False.
A product of prime numbers is only prime if it involves exactly one prime number. When you multiply two or more prime numbers together, the result is always a composite number, not a prime. As this number has 2 factors now.
(c) False.
Prime numbers have exactly two factors 1 and itself.
(d) False.
The number 2 is an even number, but it is not composite. As it is a prime number.
(e) True.
For every prime number greater than 2, the next number is composite.

(a) The prime factorization of 64 is 2 × 2 × 2 × 2 × 2 × 2.
(b) The prime factorization of 104 is 2 × 2 × 2 × 13.
(c ) The prime factorization of 105 is 3 × 5 × 7.
(d) The prime factorization of 243 is 3 × 3 × 3 × 3 × 3.
(e) The prime factorization of 320 is 2 × 2 × 2 × 2 × 2 × 2 × 5.
(j) The prime factorization of 141 is 3 × 47.
(g) The prime factorization of 1728 is 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3.
(h) The prime factorization of 729 is 3 × 3 × 3 × 3 × 3 × 3.
(f) The prime factorization of 1024 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.
(j) The prime factorization of 1331 is 11 × 11 × 11.
(k) The prime factorization of 1000 is 2 × 2 × 2 × 5 × 5 × 5.

To find the smallest difference between two successive prime numbers up to 100, let’s list the prime numbers in that range and calculate the differences between each pair: Prime numbers up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Differences between successive primes:
• 3 – 2 = 1
• 5 – 3 = 2
• 7 – 5 = 2
• 11 – 7 = 4
• 13 – 11 = 2
• 17 – 13 = 4
• 19 – 17 = 2
• 23 – 19 = 4
• 29 – 23 = 6
• 31 – 29 = 2
• 37 – 31 = 6
• 41 – 37 = 4
• 43 – 41 = 2
• 47 – 43 = 4
• 53 – 47 = 6
• 59 – 53 = 6
• 61 – 59 = 2
• 67 – 61 = 6
• 71 – 67 = 4
• 73 – 71 = 2
• 79 – 73 = 6
• 83 – 79 = 4
• 89 – 83 = 6
• 97 – 89 = 8
The smallest difference between two successive primes up to 100 is 1 (between the primes 2 and 3).
The largest difference between two successive primes up to 100 is 8, which occurs between the primes 89 and 97.