Multiples, prime factors and factors

Multiples, prime factors and factors

Understanding Multiples, Factors and Prime Factors

  • A multiple of a number is the product of that number and any counting number (integers greater than zero).
  • Factors are the numbers you multiply together to get another number.
  • A prime factor is a factor that is a prime number. Prime numbers are greater than 1 and have only two factors: themselves and 1.

Identifying Multiples

  • To find the multiples of a number, you simply multiply it by any counting number. For instance, multiples of 3 include 3, 6, 9, 12, and so forth.
  • The Least Common Multiple (LCM) of two numbers is the smallest multiple that both numbers have in common.
  • Understanding multiples can help in solving problems related to common denominators, equivalent fractions, and the ordering of fractions.

Recognising Factors

  • Factors of a number include any numbers that can be multiplied together to reach that number. For example, 1, 2, 4, and 8 are factors of 8.
  • The Greatest Common Factor (GCF) is the largest number that is a factor of two or more numbers.
  • The knowledge of factors is important in simplifying fractions and solving quadratic equations.

Understanding Prime Factors

  • A prime number is a number greater than 1 that has no positive integers other than 1 and itself as factors.
  • Prime factorisation is expressing a number as a product of its prime factors.
  • For example, the prime factorisation of 12 would be 2 x 2 x 3. This can also be written as 2^2 x 3.

Practice Problems

  • Find the prime factors of 45.
    • Solution: 3 x 3 x 5
  • Identify the GCF of 24 and 36.
    • Solution: 12
  • Determine the LCM of 6 and 8.
    • Solution: 24

Review and Practice

  • A good understanding of multiples, factors and prime factors forms the basis for many topics in mathematics, including fractions and algebra.
  • You should practice identifying multiples and factors regularly to develop speed and accuracy.
  • Always remember to check your answers, especially when dealing with larger numbers. Prime factorisation can help with this.