Learn: Factors, Multiples, Primes, HCF, and LCM

Welcome!Today, we'll learn about factors, multiples, prime numbers, highest common factor (HCF), and lowest common multiple (LCM). These concepts are essential for solving problems in GCSE Mathematics. Let's dive in!

What are Factors?Factors are numbers that divide exactly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Factors are useful for simplifying fractions and finding common divisors.

What are Multiples?Multiples are numbers obtained by multiplying a given number by integers. For example, multiples of 3 are 3, 6, 9, 12, and so on. Multiples are helpful for identifying common multiples between numbers.

Prime NumbersA prime number is a number greater than 1 that has exactly two factors: 1 and itself. Examples include 2, 3, 5, 7, 11, and 13. Prime numbers are important in number theory and play a key role in many mathematical problems.

Highest Common Factor (HCF)The highest common factor (HCF) of two or more numbers is the largest number that divides all of them exactly. For example, the HCF of 12 and 18 is 6, as it is the largest number that divides both 12 and 18.

Lowest Common Multiple (LCM)The lowest common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of them. For example, the LCM of 4 and 6 is 12 because 12 is the smallest number divisible by both 4 and 6.

Finding HCF and LCMTo find the HCF, list all the factors of the given numbers and identify the largest common factor. To find the LCM, list the multiples of the numbers and identify the smallest common multiple.

Review Time!Great work! You've learned about factors, multiples, prime numbers, HCF, and LCM. Let's test your understanding with a few questions.

Well Done!You've completed the lesson on factors, multiples, primes, HCF, and LCM. Keep practising these concepts to reinforce your understanding!