Factors, Multiples and Primes Understanding the concepts of factors , multiples , and prime numbers is essential in 11-plus mathematics. This topic encompasses...
Understanding the concepts of factors, multiples, and prime numbers is essential in 11-plus mathematics. This topic encompasses identifying factors and multiples, recognizing prime numbers, and finding the highest common factor (HCF) and lowest common multiple (LCM).
A factor of a number is a whole number that divides that number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. In contrast, a multiple of a number is the product of that number and any whole number. For instance, the first few multiples of 3 are 3, 6, 9, 12, and so on.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, and 13. Notably, 2 is the only even prime number.
The highest common factor (HCF) of two or more numbers is the largest number that divides all of them without leaving a remainder. For example, to find the HCF of 12 and 16:
Problem: Find the HCF of 12 and 16.
Solution:
The lowest common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of them. For example, to find the LCM of 4 and 5:
Problem: Find the LCM of 4 and 5.
Solution:
Prime factorisation involves breaking down a number into its prime factors. For example, the prime factorisation of 18 is 2 × 3 × 3 or 2 × 3².
A square number is the product of a number multiplied by itself (e.g., 1, 4, 9, 16), while a cube number is the product of a number multiplied by itself twice (e.g., 1, 8, 27, 64).
Students will learn to apply these concepts to solve various mathematical problems, enhancing their problem-solving skills and preparing them for the 11-plus examination.