Real Numbers Problems on
Euclid's Division Algorithm(2016)
Q1(CBSE 2012): Using Euclid’s division algorithm, find the HCF of 240 and 228.
Answer: By Euclid’s division algorithm,
⇒ 240 = 228 × 1 + 12
⇒ 228 = 12 × 19 + 0
∴ HCF (240, 228) = 12
Q2(CBSE 2014): The length, breadth and height of a room are 8m 25 cm, 6m 75 cm and 4 m 50 cm respectively. Find the length of the longest rod that can measure the three dimensions of the room exactly.
Answer:
∵ 1m = 100 cm
∴ 8 m 25 cm = 825 cm
6 m 75 cm = 675 cm
4 m 50 cm = 450 cm
The length of the longest rod = HCF(825, 675, 450)
⇒ 825 = 675 × 1 + 150
675 = 150 × 4 + 75
150 = 75 × 2 + 0
∴ HCF(825, 675) = 75
450 = 75 × 6 + 0
∴ HCF(450, 75) = 75
∴ HCF (825, 675, 450) = 75×
Thus, the length of the longest rod is 75 cm.
Q3(NCERT Exemplar): Write whether every positive integer can be of the form 4q + 2, where q is an integer.Justify your answer.
Answer: No, every positive integer cannot be expressed as only of the form 4q + 2.