Natural Numbers, Factors and Multiples
Natural numbers are numbers used for counting. Common examples are one, two, three, four et cetera. All natural numbers can be written as products of factors. For example the number 6 is the product of one and six or two and three. Hence one, two, three and six are factors of the number 6. A multiple of a number is the product of its factors.
Prime Numbers & Prime Factorisation
A prime number is a whole number that has exactly two different factors, the number 1 and itself. A common example is the number 3. Since the number 3 has no other factor other than one and itself, we say that the number 3 is a prime number. Please note that one is not a prime number as it has only one factor, namely the number 1. Prime numbers have exactly two factors, not “at most two” or anything like that. Here are the first few prime numbers between 1 to 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
When a number has more than two factors it is called a composite number. Factors of a number that are also prime are known as prime factors. For example, the factors of 21 are one, three, seven and twenty-one. As such, the prime factors of 21 are three and seven. Prime factorisation is the process of expressing a composite number as the product of prime factors.
Common Factors & Multiples
When two or more numbers have factors that are the same, these factors are known as common factors. Let’s take for example the factors of the numbers 9: one, three, nine and 21: one, three, seven, twenty-one. Hence the common factors of 9 and 21 are one and three. The largest of the common factors between two or more numbers is known as the highest common factor (HCF). Using the same example of 9 and 21 as above, we can see that the highest common factor of 9 and 21 is three.
When two or more numbers have multiples that are the same, these multiples are known as common multiples. For example, the first few multiples of the numbers 2: two, four, six, eight, ten, twelve, fourteen and 4: four, eight, twelve, sixteen, twenty. Hence the first three common multiples of 2 and 4 are four, eight and twelve. The smallest of the common multiples between two or more numbers is known as the lowest common multiple. As mentioned earlier, the first three common multiples of 2 and 4 are four, eight and twelve. As such, the lowest common multiple of 2 and 4 is four.
Mastering Maths and Numbers
Learning about numbers and its different functions can sometimes be an uphill task for most students. As such, many parents sign up for courses at Maths tuition Singapore centres to guide their children in mastering Maths. Edufront is an example of a top Maths tuition centre in Singapore. If you have children who are struggling with Primary level Maths, then you should sign them up for Edufront’s popular and highly rated Primary Maths Mastery programme.