Lecture Notes: Understanding Multiples and Factors

Multiples

Definition: Multiples are essentially the times tables of a number.
Example with 6:
- First five multiples: 6, 12, 18, 24, 30.
- All multiples of a number are divisible by that number without a remainder.
- Example:
  - 18 is a multiple of 6 because 18 ÷ 6 = 3.
  - 19 is not a multiple of 6 because 19 ÷ 6 = 3 R1 (remainder 1).
Checking for Multiples:
- To check if a big number is a multiple, divide it by the target number.
- Example:
  - 378 ÷ 6 = 63, so 378 is a multiple of 6.
  - 412 ÷ 6 = 68.6 (not a whole number), so 412 is not a multiple of 6.
Alternating Method:
- Keep adding the number to find its multiples.
- Example with 14: 14, 28, 42, 56, 70, etc.

Definition: Factors are numbers that multiply together to make another number.
Factor Pairs:
- Example with 28:
  - Factor pairs: 1 x 28, 2 x 14, 4 x 7.
  - These numbers (1, 2, 4, 7, 14, 28) are factors of 28.
Checking for Factors:
- A number is a factor if it divides into another number without a remainder.
- Example:
  - 4 is a factor of 28 because 28 ÷ 4 = 7.
  - 5 is not a factor of 28 because 28 ÷ 5 = 5.6.
Finding Factors:
- List factor pairs starting with 1 and the number itself.
- Example with 48:
  - Factor pairs: 1 x 48, 2 x 24, 3 x 16, 4 x 12, 6 x 8.
  - Factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
- Example with 50:
  - Factor pairs: 1 x 50, 2 x 25, 5 x 10.
  - Factors: 1, 2, 5, 10, 25, 50.

Multiples vs. Factors:
- Multiples are larger numbers a number can multiply to.
- Factors are smaller numbers that divide into the number.
Example with 12:
- Multiples: 24, 36, 48, etc.
- Factors: 1, 2, 3, 4, 6, 12.
Important Note:
- The number itself is both a multiple and a factor.

Be clear on the difference between multiples and factors.
Remembering the number itself counts as both a multiple and a factor is essential.
Understanding these concepts will help avoid confusion during exams.

End of Lecture