What are Numbers?
When we want to know about the quantity of something –
● How do we know the quantity?
● How do we measure quantity?
● What do we use to denote the quantities?
We use numbers to denote quantity. A NUMBER is a mathematical object used to count, measure, and label things as an individual or group.
Numbers can be of two types –
● Whole numbers – All the numbers from 0 to ∞ – 0,1,2,3,4,5,6,7,8,9………………..
● Natural numbers – All the numbers from 1 to ∞ – 1,2,3,4,5,6,7,8,9…………………..
These natural numbers can be further divided into –
1. Prime Numbers – Numbers that are divisible by 1 and themselves. Example – 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
2. Composite Numbers – Numbers that are divisible by other than 1 and itself. Example – 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50
Multiple is the product of one number multiplied by another number. When we multiply 5 with 2 we get 10 as multiple of 5 and 2.Similarly the other multiples of 5 are 15, 20, 25, etc. Through multiples, it is easy to find out LCM of given numbers.
Least Common Multiple (LCM)
The smallest positive number that is a multiple of two or more numbers is called LCM.
We use LCM in the following situations –
● About an event that is or will be repeating over and over.
● To purchase or get multiple items.
● To figure out when something will happen again at the same time.
Imagine you have 2 slices of pizza remaining and you must share among 3 friends and no one wants to share their slice. Now to distribute equally –
- What do you do to share 2 slices of pizza among your 3 friends?
If we think hard we may join two pieces and cut them equally into three slices so that everyone can get a slice. But we can solve this problem easily by using some Mathematical methods and rules. For example – we can cut 2 slices into 6 slices and share them among 3 friends. Here we are finding LCM of 2 and 3 to solve the problem. After listing out the multiples of 2 and 3
● 2 = 2, 4,6,8,10,12,14,16,18,20 (Multiples of 2)
● 3 = 3,6,9,12,15,18,21,24,27,30 (Multiples 3)
So, among the common multiples, 6 is the least. Hence we can make 6 slices out of 2 large slices of the pizza to distribute the remaining 2 slices of pizza equally.
Factors are the numbers you multiply together to get another number. In other words, the numbers that divide a number without any reminder are called Factors. Example – 2 X 6 = 12, here the 2 and 6 are the factors of the number 12. There can be more than one factor or maybe no factors. The number 12 can be written as 3 X4 , 4 X 3, 6 x 2, 2 x 6, etc. The numbers like 3 have no factors other than 1 and 3. Here the groups must be formed with 3 separate individuals or whole 3 as one group, this kind of numbers which are divisible by 1 and only themselves are called Prime Factors. Using factors we can find out the HCF (Highest Common Factor) of given numbers for dividing etc.
Highest Common Factor (HCF) or Great Common divisor (GCD)
The greatest number that can divide given numbers with no reminder is called HCF or Greatest Common Divisor (GCD).
We use HCF in following situations –
● To split things into smaller sections.
● To equally distribute 2 or more sets of items into their largest grouping.
● To figure out how many people we can invite.
● To arrange something into rows or groups.
Suppose you have four buckets of 14 ltr, 28ltr, 35ltr and 49 ltr, and you have to use a container of the largest volume with which all the bucket’s water could be measured exactly. To find out the right container to measure water, we can use HCF method in the following manner –
Find Factors of volumes of each bucket –
● 14 – 1,2,7,14
● 28 – 1,2,4,7,14,28
● 35 – 1,5,7,35
● 49 – 1,7,49
Here we got 7 as the highest factor that can divide all the given numbers, so the container must be of 7 ltr to measure water exactly.
The knowledge of Numbers, Factors and Multiples is important in one’s life. Learning multiples and factors may come handy while pursuing your higher studies in Mathematics and other related disciplines. It may help you to save time while calculating, planning and dividing things. It can also enhance skills like conceptual learning and Peer learning. To learn better ways to solve problems and get a better understanding of the Numbers, Factors, and Multiples we can use learning/teaching models, charts and other visual aids.
Check our hands-on learning activity video glimpses to know more about the ‘Numbers, Factors and Multiples’ and for many more interesting activities.