Neha Tyagi and Amit Rastogi Solutions for Chapter: Real Numbers, Exercise 2: Exercise

The product of two consecutive positive integers is divisible by $2$.

'The product of three consecutive positive integers is divisible by $6$'.

A positive integer is of the form $3q+1,$ $q$ being $a$ natural number. Can you write its square in any form other than $3m+1$, $i.e., 3m$ or $3m+2$ for some integer $m$? Justify your answer.

The number $525$ and $3000$ are both divisible only by $3, 5, 15, 25$ and $75$. What is $HCF$$\left(525,3000\right)$?Justify your answer.

Explain why $3\times 5\times 7+7$ is a composite number.

Can two numbers have $18$ as their $HCF$ and $380$ as their $LCM$? Give reasons.

Without actually performing the long division, find if $\frac{987}{10500}$will have terminating or non-terminating (repeating) decimal expansion. Give reason of your answer.

A rational number in its decimal expansion is $327.7081$. What can you say about the prime factors of $q$, when this number is expressed in the form $\frac{p}{q}$? Give reasons.