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Playing With Numbers

    Introduction

    Factors and Multiples

    Prime and Composite Numbers

    Even and Odd numbers

    Tests for Divisibility of Numbers

    Prime Factorisation

    Common Factors and Common Multiples

    Exercise 3.1

    Exercise 3.2

    Exercise 3.3

    Exercise 3.4

    Exercise 3.5

    Exercise 3.6

    Exercise 3.7

    What Have We Discussed?

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

    Enhanced Curriculum Support

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Playing With Numbers > Exercise 3.7

Exercise 3.7

1. Which of the following numbers are divisible by 4?

(i) 572 (ii) 21,084 (iii) 14,560 (iv) 1,700 (v) 2150

(i) 572

Answer:

The given number is 572.

The number formed by its last two digits is .

So, the given number is divisible by .

(ii) 5,31,048

Answer:

The given number is 5,31,048.

The number formed by its last two digits is .

So, the given number is divisible by .

(iii) 5500

Answer:

The given number is 5500.

The number formed by its last two digits is .

So, the given number is divisible by .

(iv) 6136

Answer:

The given number is 6136.

The number formed by its last two digits is .

So, the given number is divisible by .

(v) 4152

Answer:

The given number is 4152.

The number formed by its last two digits is .

So, the given number is divisible by .

2. Test whether the following numbers are divisible by 8?

(i) 9774 (ii) 5,31,048 (iii) 5500 (iv) 6136 (v) 4152

(i) 9774

Answer:

The given number is 9774.

The number formed by its last three digits is .

So, the given number divisible by 8.

(ii) 5,31,048

Answer:

The given number is 5,31,048.

The number formed by its last three digits is .

So, the given number is divisible by .

(iii) 5500

Answer:

The given number is 5500.

The number formed by its last three digits is .

So, the given number is not divisible by .

(iv) 6136

Answer:

The given number is 6136.

The number formed by its last three digits is .

So, the given number is divisible by .

(v) 4152

Answer:

The given number is 4152.

The number formed by its last three digits is .

So, the given number is divisible by .

3. Check whether the following numbers are divisible by 11?

(i) 859484 (ii) 10824 (iii) 20801

(i) 859484

Answer:

The given number is 859484.

Sum of the digits at odd places = 4 + 4 + 5 =

Sum of the digits at even places = 8 + 9 + 8 =

Their difference = – =

So, the given number divisible by 11.

(ii) 10824

Answer:

The given number is 10824.

Sum of the digits at odd places = 4 + 8 + 1 =

Sum of the digits at even places = 2 + 0 =

Their difference = – =

So, the given number divisible by 11.

(iii) 20801

Answer:

The given number is 20801.

Sum of the digits at odd places = 1 + 8 + 2 =

Sum of the digits at even places = 0 + 0 =

Their difference = – =

So, the given number divisible by 11.

4. Verify whether the following numbers are divisible by 4 and by 8?

(i) 2104 (ii) 726352 (iii) 1800

(i) 2104

Answer:

The given number is 2104.

The number formed by its last two digits is .

So, the given number is divisible by .

The number formed by its last three digits is .

So, the given number divisible by 8.

(ii) 726352

Answer:

The given number is 726352.

The number formed by its last two digits is .

So, the given number is divisible by .

The number formed by its last three digits is .

So, the given number divisible by 8.

(iii) 1800

Answer:

The given number is 1800.

1800 = 1000 + 800

1000 and 800 are multiples of .

We know that 100 is divisible by .

So, the given number is divisible by .

The number formed by its last three digits is .

So, the given number divisible by 8.

5. Find the smallest number that must be added to 289279, so that it is divisible by 8?

Answer:

The given number is 289279.

The number formed by its last three digits is .

If 279 is to be exactly divisible by 8, we have to add to it.

(i.e.,) + = ; it is divisible by 8.

So, must be added to the given number, so that it is divisible by 8.

6. Find the smallest number that can be subtracted from 1965, so that it becomes divisible by 4?

Answer:

The given number is .

The number formed by its last two digits is .

The smallest number that can be subtracted from 65 is , so that it becomes divisible by 4.

(i.e.) – =

Thus, is divisible by 4.

7. Write all the possible numbers between 1000 and 1100, that are divisible by 11? Answer:

We know that is divisible by 11 (∵ 90 × 11 = ).

is a multiple of 11.

The possible numbers divisible by 11 are , , , , , , , , .

8. Write the nearest number to 1240 which is divisible by 11?

Answer:

11 × =

11 × =

The nearest number to is but not .

Therefore, is the nearest number to which is divisible by 11.

9. Write the nearest number to 105 which is divisible by 4?

Answer:

We know that 4 × 25 =

4 × =

4 × =

Therefore, is the nearest number to which is divisible by 4.