Question

175 and 1001,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 :
175 and 1001
1
Prime factors of 175 = 5² × 7¹
Prime factors of 1001 = 7¹× 11¹× 13¹
GCD (175 ,1001) = 7
LCM (175 ,1001) = 5² × 7 × 11 × 13= 25025
LCM (175 ,1001) = 25025

Hence, the GCD is 7 & LCM is 25025

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 .

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

175 = 5 × 5 × 7 = 5² × 7

1001 = 7 × 11 × 13

HCF ( 175 , 1001 ) = 7

[ Product of the smallest power of

each common prime factors of the

numbers ]

LCM ( 175 , 1001 ) = 5² × 7 × 11 × 13

[ Product of the greatest power of each

prime factors of the numbers ]

= 25025

Therefore ,

HCF = 7 ,

LCM = 25025

I hope this helps you.

: )