Coprime and Ordinal Numbers

While dividing, kids are happy to divide numbers like 2,3 and 5. It is because they are just divisible  by 1 and the number itself. Let us put all these numbers in a box and name them as prime  numbers. So the prime numbers box contains numbers that are divisible by 1 and the number  itself. 

There is one more box with the name co-prime numbers. When you look inside you get similar  numbers but they are paired. Ex. (2,3), (3,7), etc. 

Are you confused? Not to worry, these are paired based on one common factor. Consider the first  pair (2,3) the factors of 2 are {1, 2} and factors of 3 are {1, 3}. So the common factor between  them is 1. Hence this pair is a co-prime number. 

Characteristics of Co-Prime Numbers 

I’ll give you a few pairs of Co prime numbers, using them I’ll explain their characteristics. Co prime numbers – (14, 15), (2, 3), (6,8) 

• Factors of 14 = {1, 2, 7, 14} and factors of 15 = {1, 3, 5, 15}. Here the highest common  factor (HCF) = 1 similarly for the second pair also HCF is 1. So it shows that a pair of  consecutive numbers is always a co-prime number pair and its HCF is always 1.  
• In (6, 8), factors of 6 = {1, 2, 3, 6} and factors of 8 = {1, 2, 4, 8}. Here common factors are  1 and 2. It has got 2 common factors so this pair is not a co-prime number pair. Hence  even number pairs cannot make a co-prime number pair. 
• Any pair of prime numbers is a pair of co-prime numbers since HCF is 1. 
• Let us take (2, 3), 2 + 3 = 5 and 2 ✕ 3 = 6. Pair of 5 and 6 is a coprime pair. Similarly in  (14,15), 14 + 15 = 29 and 14 ✕ 15 = 210. Pair of 29 and 210 is a coprime pair. Hence the  sum and product of coprime numbers make a coprime pair. 
• In (1,3) and (1,4) you can make out both of these are co-prime numbers pairs. This means  any number if paired with 1 makes a coprime pair. 

Illustration: 

Now you might have understood all the properties of co-prime numbers. Now, let us go back to  our boxes. I’ll give you a few boxes of co-prime numbers for arranging. Arrange them along with  the first two using ordinal numbers.  

Boxes: containing pairs of prime numbers, Pairs of numbers with 1, Pairs of consecutive numbers,  Pairs of 2 same prime numbers, Pairs of prime numbers whose difference is equal to 2.  Arrangement: 

• 1st = Prime number box
• 2nd = Co prime number box 
• 3rd = Box of prime number pairs. 
• 4th = Box of Pairs of numbers with 1 
• 5th = Box of Pairs of consecutive numbers 
• 6th = Box of Pairs of prime numbers whose difference is equal to 2. 

From this arrangement, it is easy for you to find the total number of boxes and you can identify  what is there in box number 5 effortlessly. 

Ordinal Numbers 

Basically, when you define a position of something, you use ordinal numbers. List of first ten  ordinal numbers. 

1. First 
2. Second 
3. Third 
4. Fourth 
5. Fifth 
6. Sixth 
7. Seventh 
8. Eighth 
9. Ninth 
10. Tenth 

Suppose you have to arrange these boxes in order. You number the prime number box as first  and the co-prime number box as the second. The first and second shows the order of the boxes  arrangement, So the first and second are ordinal numbers.  

Ex: While speaking about a building you use the first floor, second floor, etc. to represent the  order of its floor arrangement. 

This is all about ordinal and co-prime numbers. Hope you understood properly. For more details  log on to the cuemath website.