Understanding Multiples and Factors in Math

Multiples

• Definition: Multiples are the times tables of a number.
• Examples:
  • For the number 6: First five multiples are 6, 12, 18, 24, 30.
  • Multiples of a number can be divided 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).
• Checking for Multiples:
  • Divide the big number 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:
  • Add the number repeatedly to find its multiples.
  • Example with 14: 14, 28, 42, 56, 70, etc.

Factors

• Definition: Factors are numbers that multiply together to produce 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 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.

Key Points

• Multiples vs. Factors:
  • Multiples: Larger numbers a number can multiply to.
  • Factors: 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.

Conclusion

• Understand the difference between multiples and factors.
• Remember that the number itself counts as both a multiple and a factor.
• These concepts are crucial for avoiding confusion during exams.