Question

find the longest tape which can be used to measure 1m 50 cm and 6m 50 cm

Answer 1

HCF by prime factorization method :

HCF of two or more numbers =  product of the smallest power of each common prime factor involved in the numbers

SOLUTION :

First change the length into cm.

[1m= 100cm]

1m 75 cm = 1×100 +75 = 100 +75= 175 cm

4m 50cm= 4×100+50= 450 cm

6m 50 cm= 6×100+50 = 650 cm

Find the H.C.F of 3 lengths 175 cm, 450 cm, 650 cm

HCF by prime factorization method :

175 = 5×5×7 = 5²×7

450 = 2× 5×5×11= 2 × 5² ×11

650 = 2× 5×5 ×13 = 2× 5² × 13

H.C.F= 5² =  5×5 = 25

The longest tape which can be used to measure exactly the length 175 cm, 450 cm, 650 cm  is 25 cm

Hence, the length of the longest tape which can be used to measure exactly 1m 75cm, 4m 50cm and 6m 50cm  is 25 cm.

HOPE THIS WILL HELP YOU..