Prime Time - Free MCQ Practice Test with solutions, Class 6

Common multiples are defined as numbers that can be evenly divided by two or more given numbers. For example, for the numbers 3 and 5, common multiples include 15, 30, and 45.

A factor is defined as a number that can divide another number without leaving a remainder. For instance, 4 is a factor of 12 because 12 ÷ 4 = 3.

A prime number is defined as a number greater than 1 that can be evenly divided only by 1 and itself. For example, 7 is a prime number because its only divisors are 1 and 7.

A composite number is defined as a number that has more than two factors. The number 12 is composite because it can be divided by 1, 2, 3, 4, 6, and 12.

Prime factorization refers to expressing a number as a product of its prime numbers. For example, 84 can be expressed as 2 × 2 × 3 × 7.

The unique factorization theorem states that every number greater than 1 can be expressed as a product of prime numbers in a unique way, although the order of the factors may vary.

Co-prime numbers are defined as two numbers that have no common factors other than 1. For example, 8 and 15 are co-prime because they share no prime factors.

To confirm that two numbers are co-prime, their prime factorizations must show no common prime factors. If there are no shared prime factors, they are co-prime.

A number is divisible by 5 if its last digit is either 0 or 5. This is a simple divisibility rule for identifying multiples of 5.

The divisibility rule for 2 states that a number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

A perfect square is defined as a number that is the square of an integer. For instance, 9 can be expressed as 3 × 3.

A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself. 15 has factors 1, 3, 5, 15; 22 has factors 1, 2, 11, 22; 25 has factors 1, 5, 25. Only 17 has exactly two factors (1 and 17), so it is the prime number.

A common factor is defined as a number that can evenly divide each number in a given set. For instance, the number 4 is a common factor of 12 and 16.

A number is divisible by 4 if the number formed by its last two digits is divisible by 4. This rule helps quickly determine divisibility by 4.

Prime numbers are characterized by having exactly two positive divisors: 1 and the number itself. This definition distinguishes them from composite numbers, which have more than two divisors.