Multiples and factors

• What is a multiple?


  A multiple is any integer multiplied by a number.
• How is 15 a multiple 5 in terms of multiples

  15 is a multiple of 5 because \(3 \times 5 = 15\).
• What is a factor?


  A factor is any integer that divides exactly into another number.
• How is 8 related to 24 in terms of factors?


  8 is a factor of 24 because it divides into 24 exactly \(3 \times 8\).
• What are factor pairs?


  • Factor pairs are two numbers that multiply together to make a certain number.
  • Example: For 12, the factor pairs are (1, 12), (2, 6), and (3, 4).
• List all the factors of 24.


  The factors of 24 are 1, 2, 3, 4, 6, 8, 12.
• What defines a prime number?


  A prime number has exactly two factors: 1 and itself.
• Is 11 a prime number? Why?


  Yes, because it can only be divided by 1 and 11.
• What are the prime numbers between 42 and 45?


  The prime number between 42 and 45 is 43.
• What is a square number?


  A square number is a number multiplied by itself.
• What is the value of 20 squared?


  The value of 20 squared is \(20 \times 20 = 400\).
• What is a cube number?


  A cube number is a number multiplied by itself three times.
• What is the value of \(10\) cubed?

  The value of \(10\) cubed is \(10 \times 10 \times 10 = 1000\).
• What are powers and indices?


  • Powers or indices are ways of writing numbers that have been multiplied by themselves.
  • Example: \(2 \times 2 = 2^2\).
• What is a square root?


  A square root is the reverse of a squared number.
• What is the square root of \(25\)?


  The square root of \(25\) is \(5\) because \(5^2 = 25\).
• How do you estimate the value of \(3.7^3\)?


  You estimate it by finding the cubes of nearby integers, \(3^3 = 27\) and \(4^3 = 64\), so \(3.7^3\) is between 27 and 64.
• What is a prime factor tree?


  • A prime factor tree is a diagram used to find the prime factors of a number.
  • Example: For 40, the prime factorization is \(2^3 \times 5\).
• What are the prime numbers listed in the study material?


  The prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
• What is a common factor?


  A common factor is a factor that is shared by two or more numbers.
• What is the common factor of 8 and 10?


  The common factor of 8 and 10 is 2.
• What is the highest common factor (HCF)?


  The HCF is the largest common factor shared by two or more numbers.
• What is the HCF of 8 and 12?


  The HCF of 8 and 12 is 4.
• What is a common multiple?


  A common multiple is a shared multiple of two or more numbers.
• What is the lowest common multiple (LCM) of 5 and 6?


  The LCM of 5 and 6 is 30.
• How do you find the HCF and LCM of prime factors?


  • HCF: Multiply the common prime factors together.
  • LCM: Multiply the HCF by the remaining numbers.
• What is the HCF and LCM of 24 and 180?


  The HCF is \(12\) and the LCM is \(360\).
• What are Venn diagrams used for?


  • Venn diagrams show the relationship between different sets or categories of data.
  • They help find the LCM and HCF of numbers.
• How can Venn diagrams be used with numbers?


  Venn diagrams can categorize numbers into even numbers and multiples.
• What does the intersection of sets in a Venn diagram represent?


  The intersection represents the common elements shared by the sets.