Question

4000 and 25,Find g.c.d. and Lc.m. using the fundamental theorem of arithmetic.

Answer 1

FUNDAMENTAL THEOREM OF ARITHMETIC : Every composite number can be expressed( factorized) as a product of primes and this factorization is unique except for the order in which the prime factors occur.

GCD (Greatest common divisior) (HCF) (Highest Common Factor) of two or more numbers= Product of the smallest Power of each common prime factor involved in the numbers.

LCM (least common multiple) of two or more numbers = product of the highest Power of each factor involved in the numbers.

SOLUTION :

4000 and 25

Prime factors of 4000 = 2^5 × 5³

Prime factors of 25 = 5²

GCD (4000 and 25) = 5² = 5 × 5 = 25

LCM (4000 and 25) = 2^5 × 5³ = 32 × 125= 4000

LCM (4000 and 25) = 4000

Hence, the GCD is 25 & LCM is 4000

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hi ,

*****************************************
Fundamental Theorem of Arithmetic :

Every composite number can be

expressed ( factorised ) as a product

of primes , and this factorisation is

unique , apart from the order in which

the prime factors occur.

***************************************

4000 = 2^5 × 5³

25 = 5²

HCF ( 4000 , 25 ) = 5² = 25

[ Product of the smallest power of each

common factors of the numbers ]

LCM ( 4000 , 25 ) = 5³ × 2^5

[ Product of the greatest power of

each prime factors of the numbers )

= 4000

Therefore ,

HCF ( 4000 , 25 ) = 25 ,

LCM ( 4000 , 25 ) = 4000

I hope this helps you.

: )