# NCERT Class 10 Chapter 1 Real Numbers Official CBSE Board Sample Problems: Very Short Answer

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## Question

If HCF then find LCM

### Solution

Product of numbers

LCM

## Question

If 6.249 is expressed in the form, what can you say about q?

### Solution

Since it is a terminating decimal, q is expressible in the form of where m and n are non-negative integers

## Question

If is expressed in the form what can you say about q?

### Solution

Since it is a repeating decimal, q is not expressible in the form of where m and n are non-negative integers

## Question

Can end with the digit 0, for any natural number n. Justify your answer.

### Solution

To end with 0, a number should be divisible by 10, i.e. by 2 and 5. But 15 is not divisible by 2 so can not end with digit 0

## Question

Without actual division, find the decimal representation of

## Question

State the Fundamental Theorem of Arithmetic

### Solution

Every composite number is expressible as a product of its prime factors. This prime factorization is unique except for the order in which the prime numbers occur.

## Question

Is prime or composite? Justify

#### Solution

is composite as it is divisible by numbers other than 1 and itself

## Question

Are the smallest prime and the smallest composite numbers coprime? Justify

### Solution

Smallest prime. =2

Smallest composite = 4

HCF=2

Since they have a common factor other than 1, they are not coprime

## Question

The product of the L.C.M and H.C.F of two natural numbers is 24. The difference of two numbers is 2. Find the numbers.

### Solution

Let the numbers be a and b.

or 4

So the numbers are 4 and 6

## Question

If two positive integers a and b are expressible in the form and ; p, q being prime numbers, then find the LCM(a, b).

## Question

Let

Be a rational number. Then x has decimal expansion which terminates:

### Solution

After three places of decimal

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