Which of the following is a prime number?
a) 1
b) 111
c) 81
d) 61
Which of the following is false?
a) All even numbers except 2 are composite numbers.
b) A prime number has exactly two factors.
c) The sum of any two prime numbers is always a composite number.
d) Square numbers have an odd number of factors.
Which number is not divisible by 3?
a) 12,345
b) 19219
c) 45,678
d) 98,721
Which of the following is not a property of multiples?
a) A number cannot be a multiple of itself.
b) Every number is a multiple of each of its factors and itself.
c) Every multiple of a number is greater than or equal to that number.
d) Every number has an infinite number of multiples.
Which of the following is a perfect number?
a) 22
b) 26
c) 28
d) 20
Answer (2)
The answers to the questions are: 1) d) 61, 2) c) The sum of any two prime numbers is always a composite number, 3) b) 19219, 4) a) A number cannot be a multiple of itself, and 5) c) 28.
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Let's solve each part of the question step-by-step:
Which of the following is a prime number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Let's check each option:
a) 1: 1 is not a prime number because it does not have exactly two distinct positive divisors.
b) 111: The sum of the digits is 1 + 1 + 1 = 3, which is divisible by 3, so 111 is not a prime number.
c) 81: 81 = 9 × 9, so it is not a prime number.
d) 61: 61 cannot be divided evenly by any integer other than 1 and 61 itself, making it a prime number.
The correct answer is d) 61 .
Which of the following is false?
Let's evaluate each statement:
a) All even numbers except 2 are composite numbers: True.
b) A prime number has exactly two factors: True.
c) The sum of any two prime numbers is always a composite number: False. For example, the sum of the prime numbers 2 and 3 is 5, which is prime.
d) Square numbers have an odd number of factors: True.
The false statement is c) The sum of any two prime numbers is always a composite number .
Which number is not divisible by 3?
To determine divisibility by 3, sum the digits of each number; if that sum is divisible by 3, the number itself is divisible by 3.
a) 12,345: 1 + 2 + 3 + 4 + 5 = 15, and 15 is divisible by 3.
b) 19,219: 1 + 9 + 2 + 1 + 9 = 22, and 22 is not divisible by 3.
c) 45,678: 4 + 5 + 6 + 7 + 8 = 30, and 30 is divisible by 3.
d) 98,721: 9 + 8 + 7 + 2 + 1 = 27, and 27 is divisible by 3.
The number that is not divisible by 3 is b) 19,219 .
Which of the following is not a property of multiples?
Let's consider each property:
a) A number cannot be a multiple of itself: False, because by definition, every number is a multiple of itself.
b) Every number is a multiple of each of its factors and itself: True.
c) Every multiple of a number is greater than or equal to that number: True.
d) Every number has an infinite number of multiples: True.
The statement that is not a property of multiples is a) A number cannot be a multiple of itself .
Which of the following is a perfect number?
A perfect number is a positive integer that is equal to the sum of its proper positive divisors, excluding the number itself.
a) 22: 1 + 2 + 11 = 14, not 22.
b) 26: 1 + 2 + 13 = 16, not 26.
c) 28: 1 + 2 + 4 + 7 + 14 = 28, which is a perfect number.
d) 20: 1 + 2 + 4 + 5 + 10 = 22, not 20.
The perfect number is c) 28 .
