Highest common factor (HCF) Factor pairs Multiples Factorised Product of prime numbers (or prime factorisation) Common factor Prime number Composite number Factors The factors of a positive integer are the positive integers which divide exactly into it. A prime number is a natural number which has exactly two different factors. A composite number is a natural number which has more than two factors. For example, the only two factors of 3 are 3 and 1, and of 11 are 11 and 1. 8 is a composite number since it has four factors: 1, 2, 4, and 8. For example, the factors of 8 and 1, 2, 4, and 8 since 8 ÷ 1 = 8 8÷2=4 8÷4=2 and 8÷8=1 To express a composite number as the product of prime numbers, we systematically divide the number by the prime numbers which are its factors. When we write a number as a product of factors, we say it is factorised. A number which is a factor of two or more other numbers is called a common factor of those numbers. 10 may be factorised as a product of two factors in two ways: 1 x 10 or 2 x 5. For example, 5 is a common factor of 25 and 35. We can find the highest common factor (HCF) of two or more natural numbers by first expressing then as the product of prime factors. The multiples of any whole number have the number as a factor. They are obtained by multiplying the numbers by 1, then 2, then 3, then 4, and so on. All positive integers can be split into factor pairs. For example: 8 = 8 x 1 or 2 x 4 The multiples of 10 are 1 x 10, 2 x 10, 3 x 10, 4 x 10, 5 x 10, … or 10, 20, 30, 40, 50, … Likewise, the multiples of 15 are 15, 30, 45, 60, 75, … Product Consecutive numbers Exponential notation Odd number The rules for order of operations to evaluate (or simplify) an expression Consecutive even & consecutive odd numbers Common multiple Lowest common multiple (LCM) Even number The number 30 is a multiple of both 10 and 15, so we say 30 is a common multiple of 10 and 15. The lowest common multiple (LCM) of two or more numbers is the smallest number which is a multiple of each of those numbers. A whole number is even if it has a 2 as a factor and thus is divisible by 2. A whole number is odd if it is not divisible by 2. Perform operations within Brackets first. Calculate any part involving Exponents. Starting from the left, perform all Divisions and Multiplications as you come to them. Finally, working from the left, perform all Additions and Subtractions. The word BEDMAS may help you remember this order. An amount obtained as a result of multiplying numbers. Consecutive numbers are numbers in counting order, without gaps. One example of four consecutive numbers is 6, 7, 8, 9. Consecutive even numbers are even numbers that come in a row. Consecutive odd numbers are odd numbers that come in a row. One example of three consecutive even numbers is 6, 8, 10. One example of three consecutive odd numbers is 13, 15, 17. A convenient way to write a product of identical factors is to use exponential or index notation. For example, 2 x 2 x 2 x 2 x 3 x 3 x 3 can be written in exponential notation as 24 x 33(four factors of 2 and three factors of 3).