Factors, Multiples and Primes In 11-plus Mathematics, understanding factors , multiples , and prime numbers is crucial for building a strong foundation in numbe...
In 11-plus Mathematics, understanding factors, multiples, and prime numbers is crucial for building a strong foundation in number operations. This topic encompasses several key concepts that students must master to excel in their entrance exams.
A factor of a number is an integer that can be multiplied by another integer to produce 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 15.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, and 13. Understanding prime numbers is essential 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 12 and 16 is 4. To find the HCF, list the factors of each number and identify the largest common factor.
The lowest common multiple (LCM) is the smallest number that is a multiple of two or more numbers. For example, the LCM of 4 and 5 is 20. To find the LCM, list the multiples of each number and identify the smallest common multiple.
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). This concept is useful for finding the HCF and LCM of numbers.
Square numbers are the product of an integer multiplied by itself (e.g., 1, 4, 9, 16, 25), while cube numbers are the product of an integer multiplied by itself twice (e.g., 1, 8, 27, 64). Recognising these numbers helps in various mathematical calculations.
Students will learn to apply these concepts in problem-solving scenarios. For instance, they may be asked to find the HCF and LCM of given numbers or to identify prime numbers within a specific range. Mastery of these topics will enhance their mathematical reasoning and prepare them for the challenges of the 11-plus exams.
Problem: Find the HCF and LCM of 24 and 36.
Solution: