Mahabir Singh Solutions for Chapter: Playing with Numbers, Exercise 3: ACHIEVERS SECTION (HOTS)

1. If an even number is divided by $2$, then the quotient is always odd.
2. All even numbers are composite numbers.
3. The L.C.M of two co-prime numbers cannot be equal to their product.
4. Every number is a factor of itself.

Statement- $1$: A number for which sum of all its factors is equal to twice the number is called a perfect number.
Statement- $2$: If two numbers are divisible by a number, then their sum and difference are also divisible by that number.
Which of the following options holds?

1. The H.C.F of two co-prime numbers is $\mathrm{P}$.
2. Two natural numbers which have no common factor except $1$ are called $\mathrm{Q}$ numbers.
3. If a number is divisible by $9$, then sum of its digits must be divisible by $\mathrm{R}$.

Find the value of $a\mathit{+}b\mathit{+}c$, if $373a$ is divisible by $9, 473b$ is divisible by $11$and $371c$ is divisible by $6.$

Match the following.