Class 10 Maths- Application of Fundamental Theorem of Arithmetic:

Application of Fundamental Theorem of Arithmetic:

 Fundamental theorem of arithmetic states:

Every composite number can be expressed (factorised) as a product of primes, and this factorization is unique except for the order in which the prime factors occur.

We will now learn the various applications of the fundamental theorem of arithmetic. It is used to find the HCF and LCM of two or more positive integers

Example: 

Greatest Common Measure or H.C.F of 36, 90, 72.

Step1: Express the numbers as product of prime factors.

36 = 2² × 3² 

90 = 2 × 5 × 3² 

72 = 2³ × 3² 

Step 2: Take the prime numbers with least power and is present in all sets.

2 and 3 are the prime numbers common to all given numbers.

The least power of 2 in the set is – 2

The least power of 3 in the set is - 3²

Step 3: Product of the numbers taken.

3² × 2 = 9 × 2 = 18

Therefore, 18 is the H.C.F of 36, 90, 72.

Now let’s discuss LCM.

When would you use lowest common multiples (LCM) in daily life?

Let’s say you ran a car manufacturing plant that used special screws to hold its car motors together. The screws come in packages of 8, and the motors come in packages of 10. You don't want a lot of extra screws around, because they are very expensive. So you wonder- at what point do the screws and motors match up in packages of 8 and 10? That way you can order them in even amounts.

The answer is 40, because 5 x 8 and 4 x 10 both = 40.