8th Maths : Chapter 7 : Information Processing : Exercise 7.2 : Text Book Back Numerical problems, Exercises Questions with Answers, Solution

**Exercise 7.2**

** **

**1. Using repeated division method, find
the HCF of the following:**

**(i) 455 and 26 **

**(ii) 392 and 256 **

**(iii) 6765 and 610 **

**(iv) 184, 230 and 276**

**(i) 455 and 26**

**Solution: **

**Step 1:** The larger number should be
dividend = 455

& smaller number should be divisor = 26

**Step 2:** After 1st division, the
remainder becomes new divisor & the previous divisor becomes next dividend.

**Step 3:** This is done till remainder is
zero.

**Step 4:** The last divisor is the HCF

∴ Answer: **The HCF is 13.**

**(ii) 392 and 256**

**Solution:**

256 is smaller, so it is the 1st divisor

** 8 is the last divisor
& hence the HCF.**

**∴ ****HCF = 8**

**(iii) 6765 and 610**

**Solution:**

**5 is the last divisor & hence the HCF**

**∴ ****HCF = 5**

**(iv) 184, 230 and 276**

**Solution:**

First let us take 184 & 230

**46 - Last divisor is the HCF**

**46 is the HCF of
184, and 230.**

Now the HCF of the first two numbers is the dividend for the
third number.

**∴**** Answer:** HCF of 184, 230 & 276 is 46

** **

**2. Using repeated subtraction method,
find the HCF of the following:**

**(i) 42 and 70 **

**(ii) 36 and 80 **

**(iii) 280 and 420 **

**(iv) 1014 and 654**

**(i) 42 and 70**

**Solution:**

Let number be *m* & *n* *m* > *n*

We do *m* − *n* & the result of subtraction
becomes new '*m*'. if m becomes less than *n*, we do *n* − *m*
and then assign the result as *n*. We should do this till *m* = *n*.
When *m* = *n* then '*m*’ is the HCF.

42 and 70 *m*
= 70, *n* = 42

70 – 42 = 28, now *m* = 42, *n* = 28

42 − 28 = 14, now *m* =
28, *n* = 14

28 – 14 = 14, now *m* = 14, *n*
= 14 ; we stop here as *m* = *n*

∴ HCF of 42 & 70 is 14

**(ii) 36 and 80**

**Solution:**

36 and 80 *m
*= 80, *n* = 36

80 − 36 = 44, now *n* = 44, *m*
= 36

Since *n* > *m*, we should do *n* − *m*

44 − 36 = 8, now *n* = 8, *m*
= 36

36 − 8 = 28 Similarly, processing, proceeding, we do
repeated subtraction till *m* = *n*

28 − 8 = 20

20 – 8 = 12

12 − 8 = 4

8 − 4 = 4 now *m* = *n* = 4 ∴ HCF is 4

**(iii) 280 and 420**

**Solution:**

Let *m* = 420, *n* = 280

*m* − *n* = 420 – 280 = 140

now *m* = 280, *n* = 140

*m* − *n* = 280 – 140 = 140

now *m* = *n* = 140

∴ HCF is 140

**(iv) 1014 and 654**

**Solution:**

Let *m* = 1014, *n* = 654

*m − n* = 1014 − 654 = 360

now *m* = 654, *n* = 360

*m − n* = 654 − 360 = 294

now *m* = 360, *n* = 294

*m − n* = 360 − 294 = 66

now *m* = 294, *n* = 66

*m − n* = 294 − 66 = 228

now *m* = 66, *n* = 228

*n − m* = 228 – 66 = 162

now *m* = 162, *n* = 66

∴ *m − n* = 162 − 66
= 96

*n − m* = 96 − 66 = 30

Similarly, 66−30 = 36

36 − 30 = 6

30 − 6 = 24

24 − 6 = 18

18 − 6 = 12

12 − 6 = 6 now *m = n*

∴ HCF of 1014 and 654 is 6

** **

**3. Do the given problems by repeated
subtraction method and verify the result.**

**(i) 56 and 12 **

**(ii) 320, 120 and 95 **

**(i) 56 and 12**

**Solution:**

56 & 12

Let *n* = 56 & *n* = 12

*m − n* = 56 − 12 = 44

now *m* = 44, *n* = 12

*m − n* = 44 − 12 = 32

*m − n* = 32 − 12 = 20

*m − n* = 20 − 12 = 8

*n − m* = 12 − 8 = 4

*m − n* = 8 − 4 = 4. now *m = n*

∴ **HCF of 56 & 12 is 4**

**(ii) 320, 120 and 95 **

**Solution:**

Let us take 320 & 120 first *m* = 320, *n* = 120

*m − n* = 320 − 120 = 200

*m* = 200, *n* = 120

∴ *m − n* = 200 − 120 = 80

120 − 80 = 40

80 − 40 = 40

∴ *m* = *n* = 40 → HCF of 320, 120

Now let us find HCF of 40 & 95

*m *= 95, *n* = 40

∴ *m − n* = 95 − 40 = 55

55 − 40 = 15

40 − 15 = 25

25 − 15 = 10

15 − 10 = 5 HCF of 40 & 95 is 5

10 − 5 = 5

∴ **HCF of 320, 120 & 95 is 5**

** **

**4. Kalai wants to cut identical squares
as big as she can, from a piece of paper measuring 168mm and by 196mm. What is the
length of the side of the biggest square? (To find HCF using repeated subtraction
method)**

**Solution:**

Sides are 168 & 196

To find HCF of 168 & 196, we are to use repeated subtraction
method.

∴ *m* = 196, *n* = 168

*m − n* = 196 − 168 = 28 now *n* = 28, *m* = 168

*m − n* = 168 – 28 = 140 now *m* = 140, *n* = 28

*m − n* = 140 – 28 = 112 now *m* = 112, *n* = 28

*m − n* = 112 − 28 = 84 now *m* = 84, *n* = 28

*m − n* = 84 − 28 = 56 now *m* = 56, *n* = 28

*m − n* = 56 − 28 = 28

∴ HCF is 28

∴ Length of biggest square is 28

** **

**Objective
Type Questions**

** **

**5. What is the eleventh Fibonacci number?**

(a) 55

(b) 77

(c) 89

(d) 144

**[Answer: (c) 89]**

**Solution:**

∴ 11^{th} Fibonacci number is 89

**6. If F(n) is a Fibonacci number and
n =8, which of the following is true?**

(a) F(8)
= F(9)+F(10)

(b) F(8)
= F(7)+F(6)

(c) F(8)
= F(10)×F(9)

(d) F(8)
= F(7)–F(6)

**[Answer: (b) F(8) = F(7) + F(6)]**

**Solution:**

Given F(*n*) is a Fibonacci number & *n* = 8

∴ F(8) = F(7) + F (6) as any term in Fibonacci series is the sum
of preceding 2 terms

**7. Every 3rd number of the Fibonacci
sequence is a multiple of _______**

(a) 2

(b) 3

(c) 5

(d) 8

**[Answer: (a) 2]**

**Solution: **Every 3^{rd} number in
Fibonacci sequence is a multiple of 2

**8. Every _______ number of the Fibonacci
sequence is a multiple of 8**

(a) 2nd

(b) 4th

(c) 6th

(d) 8th

**[Answer: (c) 6 ^{th}]**

**9. The difference between the 18th and
17th Fibonacci number is **

(a) 233

(b) 377

(c) 610

(d) 987

**[Answer: (d) 987]**

**Solution: **

F(18) = F(17) + F(16)

F(18) − F(17) = F(16) = F(15) + F(14)

= 610 + 377 = 987

**10. Common prime factors of 30 and 250
are **

(a) 2 × 5

(b) 3 × 5

(c) 2 × 3
× 5

(d) 5 × 5

**[Answer: (a) 2 ****× 5] **

**Solution: **

Prime factors of 30 are 2 × 3 × 5

Prime factors of 250 are 5 × 5 × 5 × 2

∴ Common prime factors are
2 × 5

**11. Common prime factors of 36, 60 and
72 are **

(a) 2 × 2

(b) 2 × 3

(c) 3 × 3

(d) 3 × 2
× 2

**[Answer: (d) 3 × 2 × 2]**

**Solution: **

Prime factors of 36 are 2 × 2 × 3 × 3

Prime factors of 60 are 2 × 2 × 3 × 5

Prime factors of 72 are 2 × 2 × 2 × 3 × 3

∴ Common prime factors are
2 × 2 × 3

**12. Two numbers are said to be co-prime
numbers if their HCF is **

(a) 2

(b) 3

(c) 0

(d) 1

**[Answer: (d)** **1]**

**Answer:**

**Exercise 7.2 **

**1. (i) 13 (ii) 8 (iii)
5 (iv) 46 **

**2. (i) 14 (ii) 4 (iii)
140 (iv) 6 **

**3. (i) 4 (ii) 5 **

**4. 14 **

**5. 28 **

**6. (C) 89 **

**7) (B) F(8) =
F(7)+F(6) **

**8. (A) 2 **

**9. (C) 6th **

**10) (D) 987**

**11. (A) 2×5 **

**12. (D) 3×2×2 not (B) 2×3 **

**13. (D) 1**

** **

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