Exploring Multiples and Factors

Exploring Multiples

• A multiple is the product of a number and any whole number.
• To find multiples of a number, multiply it by consecutive whole numbers.
• 560 is not a multiple of 11 because it's not divisible by 11.
• Multiples between 50-100 of 2 are 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100.
• Multiples greater than 100 of 2 are 102, 104, 106, 108...

Exploring Factors

• A factor is a number that divides evenly into another number.
• Use a T-table to list all the pairs of numbers that multiply to give the target number.
• All possible combinations can be found by listing all the factors and their combinations.
• The dimensions of a rectangle are its length and width, which are also factors of its area.
• 323 does not have 4 as a factor because it is not divisible by 4.
• 9 is not a factor of 463 because it doesn’t divide evenly into it.
• To group 356 attendees, find all the factors of 356 and their corresponding combinations.

Factoring into Prime Numbers

• Prime factorization is the process of breaking down a number into its prime factors.
• Use subsequent division to find the prime factorization of a number (continuously divide by prime numbers until you reach a prime number).

Common Factors and the GCF (Greatest Common Factor)

• Common factors are numbers that are factors of two or more numbers.
• The GCF is the greatest of the common factors.
• For a set of numbers, find their GCF by listing all the common factors and selecting the largest one.
• Numbers are relatively prime or co-prime when their greatest common factor is 1.
• Use subsequent division to find the GCF by repeatedly dividing the larger number by the smaller number until you arrive at a remainder of zero. The last non-zero remainder is the GCF.

Common Multiples and the LCM (Least Common Multiple)

• Common multiples are numbers that are multiples of two or more numbers.
• The LCM is the smallest of the common multiples.
• For a set of numbers, find the LCM:
  • Find their common multiples by multiplying them by increasing whole numbers.
  • The smallest common multiple is the LCM.
• Use subsequent division to find the LCM:
  • Divide the larger number by the smaller number.
  • Repeat division until you find a quotient that is a prime number.
  • Multiply the quotient by the numbers you divided by in the process.

This quiz covers the essential concepts of multiples and factors in mathematics. You'll learn how to identify multiples of a number and understand factors as numbers that divide evenly into others. Challenge yourself with examples and applications, including practical scenarios like dimensions and groupings.