Page 29 - classs 6 a_Neat

EXAMPLE 14: The length, breadth and height of a room are 1050 cm, 750 cm and 425 cm respectively. Find
the length of the longest tape which can measure the three dimensions of the room exactly. PRACTICE EXERCISE 2.4
SOLUTION: The length of the longest tape which can measure the given length
HCF of 1050 cm, 750 cm and 425 cm. 1. Write the prime factors of the following numbers.
First we find the HCF of 1050 and 750. a.49 b. 216 c. 312 d. 1024 e. 8000
750 1050 1 2. Complete the factor tree using prime numbers.
- 750

300 750 2 a. b.
- 600
150 300 2
- 300
×
Thus the HCF of 1050 and 750 = 150.
Now, we fing the HCF of 150 and 425.
150 425 7
- 300
125 150 1
- 125
25 125 5
- 125
×
Hence, HCF of 150 and 425 is 25.
Thus, the HCF of 1050, 750 and 425 is 25. c. d.
Hence, the requrid length = 25 cm.

JUST TRY:1 Find the prime factors of 30.
JUST TRY:2 Find the prime factors of 56.
JUST TRY :3 Find the prime factors of 216.
JUST TRY:4 Find the prime factors of 375.
JUST TRY:5 Find the HCF of 36 and 60 by the prime factorisation method.
JUST TRY: 6 Find the HCF of 42, 63 and 105.
JUST TRY: 7 Find the HCF of 36 and 60 by the prime factorisation method.
JUST TRY: 8 Find the HCF of 42, 63 and 105.
JUST TRY: 9 Find the HCF of 144 and 372 by the long division method.
JUST TRY: 10 Find the HCF of 75,225 and 675 by the long division method.
JUST TRY: 11 Find the greatest number which divides 245 and 1,029 leaving a remainder of e.
5 in each case.