What are common multiples, and how are they defined using the numbers 3 and 5?

Common multiples are numbers that are multiples of two or more numbers. For example, the common multiples of 3 and 5 are 15, 30, 45, etc., because these numbers can be divided by both 3 and 5 without leaving any remainder.

Common factors of two numbers are defined as numbers that ___ both numbers exactly without leaving a remainder.

Divide

In the Idli-Vada game, what should a player say when they reach a number that is a multiple of both 3 and 5?

The player should say 'idli-vada!'

True or False: The game 'Idli-Vada' continues until all players successfully say the correct numbers without mistakes.

False. The game continues until someone makes a mistake.

In the context of the Idli-Vada game, what does a player say when they reach a number that is a multiple of 3?

The player says 'idli.'

Riddle: I am a number that is a multiple of both 3 and 5, and I come before 20. What number am I?

15

Define the role of prime numbers in solving mathematical problems.

Prime numbers are essential in mathematics because they serve as the building blocks of all natural numbers, allowing us to understand factors, multiples, and number theory.

Fill in the blank: The common factors of 14 and 36 are ___ and ___.

1 and 2

What do you say when you encounter a multiple of 3 in the game?

You say 'idli' when you encounter a multiple of 3.

In the game 'Jump Jackpot', what must Jumpy do to win the treasure?

Jumpy must land exactly on the number where the treasure is hidden.

Common multiples of 3 and 5 include numbers such as ___ and ___.

15 and 30 are common multiples of 3 and 5.

True or False: If Jumpy picks 6, he can land on both treasures at 14 and 36.

False. If Jumpy picks 6, he can land on 36 but not on 14.

Which numbers are common factors of 14 and 36?

1 and 2 are common factors of 14 and 36.

Fill in the blank: In the game, multiples of 5 are recognized by saying ___.

'vada' is said for multiples of 5.

Riddle: I am a number that is both a multiple of 3 and 5. What am I?

You could be 15, 30, or any multiple of 15.

What is a common multiple of the numbers 3 and 5?

A common multiple of 3 and 5 is 15.

What happens if Jumpy chooses a number that is not a common factor of both treasures?

He will only land on one treasure and miss the other.

Identify the multiples of 4 that allow Jumpy to land on 24.

The multiples of 4 that lead to 24 are 4, 8, 12, 16, 20, and 24.

A prime number is defined as a number greater than 1 that can only be divided evenly by ___ and ___ .

1 and itself

True or False: The number 1 is classified as a prime number.

False. The number 1 is neither a prime nor a composite number.

What distinguishes a composite number from a prime number?

A composite number has more than two factors, while a prime number has exactly two factors.

Fill in the blank: An example of a prime number is ___.

7

Riddle: I am a number that can only be divided by 1 and myself, and I am greater than 1. What number am I?

A prime number

List three examples of composite numbers.

4, 6, 12

Using the Sieve of Eratosthenes, how would you identify prime numbers between 1 and 100?

You eliminate all multiples of each prime starting from 2, leaving only prime numbers.