The values of the remainder r, when a positive integer a is divided by 3 are 0 and 1 only. Justify your answer
Solution:
No,
Euclid’s Division Lemma (lemma is similar to a theorem) says that, for given two positive integers, 'a' and 'b', there exist unique integers, 'q' and 'r', such that: a = bq + r, where 0 ≤ r < b.
Using the Euclid’s division lemma,
a = 3q + r, where 0 ≤ r < 3 and r is an integer
Therefore, the values of r can be 0, 1 or 2.
✦ Try This: What is the HCF of 4052 and 12576
12576 is greater than 4052.
Applying Euclid’s division algorithm,
12576 = 4052 × 3 + 420
4052 = 420 × 9 + 272
272 = 148 × 1 + 124
148 = 124 × 1 + 24
124 = 24 × 5 + 4
24 = 4 × 6 + 0
Therefore, the HCF of 4052 and 12576 is 4
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1
NCERT Exemplar Class 10 Maths Exercise 1.2 Sample Problem 1
The values of the remainder r, when a positive integer a is divided by 3 are 0 and 1 only. Justify your answer
Summary:
The values of the remainder r, when a positive integer a is divided by 3 are 0 and 1 or 2
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