Factors and Multiples

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Factors

  1. Definition: Factors of a number are integers that can be multiplied together to get that number.
  2. Key Point: A factor divides the number evenly, with no remainder.

Finding Factors

  • Method: List all the numbers that can be multiplied together to get the original number.
  • Example: Factors of 12
    • Pairs of numbers that multiply to 12: (1 and 12), (2 and 6), (3 and 4).
    • So, the factors of 12 are 1, 2, 3, 4, 6, 12.

Real-Life Example of Factors

  • Organizing Items: Imagine you have 12 apples and want to arrange them into equal rows. The factors of 12 (1, 2, 3, 4, 6, 12) are the possible numbers of apples you can have in each row. For example, you could have 4 rows with 3 apples in each.

Multiples

  1. Definition: Multiples of a number are what you get when you multiply that number by an integer.
  2. Key Point: Multiples can be thought of as the “extended” times table of a number.

Finding Multiples

  • Method: Multiply the number by integers (1, 2, 3, 4, etc.).
  • Example: First few multiples of 5
    • 5 × 1 = 5, 5 × 2 = 10, 5 × 3 = 15, 5 × 4 = 20, and so on.
    • So, the first few multiples of 5 are 5, 10, 15, 20, etc.

Real-Life Example of Multiples

  • Time Intervals: If a bus arrives every 10 minutes, the multiples of 10 (10, 20, 30, etc.) represent the minutes at which the bus arrives. For instance, if the first bus is at 10 minutes, the next will be at 20 minutes, then 30 minutes, and so on.

Differences Between Factors and Multiples

  • Factors are numbers that divide the original number without leaving a remainder. They are always less than or equal to the original number.
  • Multiples are numbers that you get by multiplying the original number. They are equal to or greater than the original number.

Applying Factors and Multiples in Real Life

  1. Factors for Problem-Solving: If you’re dividing a set of items (like gifts or snacks) evenly among a group of people, you’d look for factors of the total number of items to know how many people you can divide them among without leftovers.
  2. Multiples in Scheduling: When planning events at regular intervals (like classes or meetings), multiples help in scheduling them at consistent times throughout the day or week.

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