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## Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 2 Chapter 4 Information Processing Ex 4.2

The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

Question 1.

Choose the correct answer

Question (i)

Common prime factors of 30 and 250 are

(a) 2 x 5

(b) 3 x 5

(c) 2 x 3 x 5

(d) 5 x 5

Answer:

(a) 2 x 5

Hint:

Prime factors of 30 are 2 x 3 x 5

Prime factors of 250 are 5 x 5 x 5 x 2

∴ Common prime factors are 2 x 5

The Prime Factorization of 84 is 22 × 3 × 7.

Question (ii)

Common prime factors of 36, 60 and 72 are

(a) 2 x 2

(b) 2 x 3

(c) 3 x 3

(d) 3 x 2 x 2

Answer:

(d) 3 x 2 x 2

Hint:

Prime factors of 36 are 2 x 2 x 3 x 3

Prime factors of 60 are 2 x 2 x 3 x 5

Prime factors of 72 are 2 x 2 x 2 x 3 x 3

∴ Common prime factors are 2 x 2 x 3

Question (iii)

Two numbers are said to be co-prime numbers if their HCF is –

(a) 2

(b) 3

(c) 0

(d) 1

Answer:

(d) 1

What is the greatest common factor of 12 and 18? Prealgebra Greatest Common Factor.

Question 2.

Using repeated division method find HCF of the following:

- 455 and 26
- 392 and 256
- 6765 and 610
- 184, 230 and 276

1. 455 and 26 divisor

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.

2. 392 and 256

256 is smaller, so it is the 1st divisor

∴ HCF = 8

3. 6765 and 610

∴ HCF = 5

4. 184, 230 and 276

First let us take 184 & 230

∴ 46 is the Hi 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

Question 3.

Using repeated subtracting method find HCF of the following:

- 42 and 70
- 36 and 80
- 280 and 420
- 1014 and 654

1. 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 now 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

2. 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

3. 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

4. 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

Question 4.

Do the given problems in repeated subtraction method

1. 56 and 12

2. 320,120 and 95

1. 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 – 44. now m = n

HCF of 56 & 12 is 4

2. 320, 120 and 95

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 = w = 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

Question 5.

On a school trip, 56 girls and 98 boys went to Kanyakumari. They were divided into as many groups as possible so that there were equal numbers of girls and boys in each group. Find the largest group possible? (To find the HCF using repeated division method)

Solution:

56 girls & 98 boys. Now, we need to find HCF of 56 & 98

Using repeated division method. So, we first divide. 98 by 56

Answer:

14.

Question 6.

Kalai wants to cut identical squares as big as she can, from a piece of paper measuring 168 mm and by 196 mm. 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