Advertisements
Advertisements
Question
Find all positive integers, when divided by 3 leaves remainder 2
Solution
All the positive integers when divided by 3 leaves remainder 2
By Euclid’s division lemma
a = bq + r, 0 ≤ r ≤ b
Here a = 3q + r where 0 < q < 3
a leaves remainder 2 when divided by 3
∴ The positive integers are 2, 5, 8, 11, …
APPEARS IN
RELATED QUESTIONS
Prove that the product of two consecutive positive integers is divisible by 2.
Show that any positive odd integer is of the form 6q + 1 or, 6q + 3 or, 6q + 5, where q is some integer.
Using Euclid’s algorithm, find the HCF of 405 and 2520 .
If a and b are relatively prime, what is their LCM?
The LCM of two numbers is 1200, show that the HCF of these numbers cannot be 500. Why ?
Show that the following numbers are irrational.
Show that \[5 - 2\sqrt{3}\] is an irrational number.
What is a composite number?
The HCF of 95 and 152, is
Show that the square of any odd integer is of the form 4q + 1, for some integer q.
