Factors, Multiples and Primes Understanding the concepts of factors , multiples , and prime numbers is essential in 11-plus Mathematics. This topic also covers...
Understanding the concepts of factors, multiples, and prime numbers is essential in 11-plus Mathematics. This topic also covers finding the highest common factor (HCF) and the lowest common multiple (LCM), as well as prime factorisation and recognizing square and cube numbers.
A factor of a number is an integer that can be multiplied by another integer to yield that number. 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 an integer. 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. Examples include 2, 3, 5, 7, and 11. Understanding prime numbers is crucial for various mathematical applications, including prime factorisation.
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, the HCF of 8 and 12 is 4.
The lowest common multiple (LCM) is the smallest multiple that is exactly divisible by two or more numbers. For instance, the LCM of 4 and 5 is 20.
Prime factorisation involves breaking down a composite number into its prime factors. For example, the prime factorisation of 18 is 2 × 3 × 3 or 2 × 3².
Square numbers are the result of multiplying an integer by itself (e.g., 1, 4, 9, 16, 25). Cube numbers are the result of multiplying an integer by itself twice (e.g., 1, 8, 27, 64).
Students will learn to apply these concepts in various problem-solving scenarios. For example, they may be asked to find the HCF and LCM of given numbers or to express a number as a product of its prime factors.
Problem: Find the HCF and LCM of 18 and 24.
Solution: