Multiples, Factors, and Prime Numbers

Multiples and Factors

• Multiples of a number are the products of that number and counting numbers.
• Every number is a multiple of itself and 1.
• There's no limit to the number of multiples of a number.
• Every multiple of a number is greater than or equal to the number.
• Factors of a product are the numbers that are multiplied to get that product.
• Every number is a factor of itself.
• 1 is a factor of every number.
• The factor of a number is less than or equal to the number.

Prime Numbers and Composite Numbers

• A prime number is divisible only by 1 and itself.
• A composite number has at least one factor other than 1 and itself.
• 2 is the only even prime number.

Coprime Numbers

• Two numbers that have only 1 as a common factor are known as coprime numbers.
• All pairs of prime numbers are coprime numbers.
• Pairs of composite numbers can also be coprime numbers.
• The number 1 is neither prime nor composite.
• All consecutive numbers are coprime.

Divisibility Rules

• Divisibility by 2: The ones digit is 0, 2, 4, 6, or 8.
• Divisibility by 3: The sum of all digits is divisible by 3.
• Divisibility by 4: The number formed by the last two digits is divisible by 4.
• Divisibility by 5: The ones digit is 0 or 5.
• Divisibility by 6: The number is divisible by both 2 and 3.
• Divisibility by 9: The sum of all digits is divisible by 9.
• Divisibility by 10: The ones digit is 0.

Highest Common Factor (HCF)

• The HCF of two numbers is the greatest number that divides both numbers exactly.
• Method 1: Prime factorization method
• Method 2: Common division method

Lowest Common Multiple (LCM)

• The LCM of two numbers is the smallest number that is divisible by both numbers exactly.
• Method 1: Listing the multiples
• Method 2: Prime factorization method

Fractions

• A fraction represents a part of a whole.
• Proper fraction: Numerator is less than the denominator.
• Improper fraction: Numerator is greater than or equal to the denominator.
• Mixed fraction: Combination of a whole number and a proper fraction.
• Equivalent fractions: Fractions that represent the same portion of a whole.
• Comparing fractions with the same denominator: Larger numerator indicates a larger fraction.
• Comparing unlike fractions: Convert unlike fractions to like fractions (common denominator).
• Compare whole parts first, then remaining fractional parts.

Explore the concepts of multiples, factors, prime numbers, and coprime numbers in this quiz. Understand how these mathematical properties interact and their definitions. Test your knowledge of these foundational topics in number theory.