Factors and Multiples of Large Numbers

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What Are Factors?

Factors of a number are numbers that can be multiplied together to get that number. For example, if we multiply 2 and 4, we get 8. So, 2 and 4 are factors of 8.

What Are Multiples?

Multiples of a number are what you get when you multiply that number by other numbers. For example, the first few multiples of 5 are 5, 10, 15, 20, and so on (because 5 x 1 = 5, 5 x 2 = 10, etc.).

Finding Factors of Large Numbers

To find factors of a large number, start by checking if it can be divided evenly by smaller numbers. For instance, to find factors of 60, see if 60 can be divided by 2, 3, 4, etc., without leaving any remainder.

Examples of Factors

  1. Factors of 36: The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. We get these by finding pairs of numbers that multiply to 36: 1 x 36, 2 x 18, 3 x 12, 4 x 9, and 6 x 6.
  2. Factors of 100: The factors of 100 include 1, 2, 4, 5, 10, 20, 25, 50, and 100. These are pairs like 1 x 100, 2 x 50, 4 x 25, 5 x 20, and so on.

Finding Multiples of Large Numbers

To find multiples of a large number, simply multiply it by 1, 2, 3, etc. Keep in mind, multiples continue infinitely.

Examples of Multiples

  1. Multiples of 25: The first few multiples of 25 are 25, 50, 75, 100, 125, and so on (25 x 1, 25 x 2, 25 x 3, etc.).
  2. Multiples of 50: For 50, the first few multiples would be 50, 100, 150, 200, 250, etc.

Real-life Examples

  1. Building Blocks: If you have 48 building blocks and want to build towers of equal height, the factors of 48 (1, 2, 3, 4, 6, 8, 12, 16, 24, 48) tell you how many blocks you can put in each tower.
  2. Arranging Chairs: If you’re arranging chairs for a party and have 30 chairs, the multiples of 30 (30, 60, 90, 120…) show you how many chairs you’ll have if you add another set of 30 chairs each time.

Tips for Understanding

  • Pairing Factors: Think of factors as pairs of numbers that work together to make the original number.
  • Multiples Keep Growing: Remember, multiples keep increasing as you multiply the number by larger numbers.
  • Use Divisibility Rules: For finding factors, it helps to know the divisibility rules (like a number is divisible by 2 if it’s even, by 5 if it ends in 5 or 0, etc.).
  • Practice with Objects: Using objects like counters or blocks can make understanding these concepts more tangible.

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