Chapter - 3 Playing with Numbers

Q&A -Ask Doubts and Get Answers

Q
Playing With Numbers

Question:

1. Find the HCF of the following numbers :

(a) 18, 48            (b) 30, 42         (c) 18, 60       (d) 27, 63

(e) 36, 84            (f) 34, 102        (g) 70, 105, 175

(h) 91, 112, 49    (i) 18, 54, 81     (j) 12, 45, 75

Solution: (a) 18, 48

Prime Factors of 18 = 2 x 3 x 3

Prime Factors of 48 = 2 x 2 x 2 x 2 x 3

H.C.F. of 18, 48 = 2 x 3=6

(b) 30, 42

Prime Factors of 30 = 2 x 3 x 5

Prime Factors of 42 = 2 x 3 x 7

H.C.F. of 30, 42 = 2 x 3 = 6

(c) 18, 60

Prime Factors of 18 = 2 x 3 x 3

Prime Factors of 60 = 2 x 2 x 3 x 5

H.C.F. of 18, 60 = 2 x 3 = 6

(d) 27, 63

Prime Factors of 27 = 3 x 3 x 3

Prime Factors of 63 = 3 x 3 x 7

H.C.F. of 27, 63 = 3 x 3 = 9

(e) 36, 84   

Prime Factors of 36 = 2 x 2 x 3 x 3

Prime Factors of 84 = 2 x 2 x 3 x 7

H.C.F. of 36, 84 = 2 x 2 x 3 = 12

(f) 34, 102

Prime Factors of 34 = 2 x 17

Prime Factors of 102 = 2 x 3 x 17

H.C.F. of 34, 102 = 2 x 17 = 34

(g) 70, 105, 175

Prime Factors of 70 = 2 x 5 x 7

Prime Factors of 105 = 3 x 5 x 7

Prime Factors of 175 = 5 x 5 x 7

H.C.F. of 70, 105, 175 = 35

(h) 91, 112, 49

Prime Factors of 91 = 7 x 13

Prime Factors of 112 = 2 x 2 x 2 x 2 x 7

Prime Factors of 49 = 7 x 7

H.C.F. of 91, 112, 49 = 1 x 7 = 7

(i) 18, 54, 81 

Prime Factors of 18 = 2 x 3 x 3

Prime Factors of 54 = 2 x 3 x 3 x 3

Prime Factors of 81 = 3 x 3 x 3 x 3

H.C.F. of 18, 54, 81 = 3 x 3 = 9

 (j) 12, 45, 75

Prime Factors of 12 = 2 x 2 x 3

Prime Factors of 45 = 3 x 3 x 5

Prime Factors of 75 = 3 x 5 x 5

H.C.F. of 12, 45, 75 = 1 x 3 = 3

 

2. What is the HCF of two consecutive

(a) numbers?      (b) even numbers?      (c) odd numbers?

Solution: (a) THe HCF of two consecutive numbers is 1.

For example: HCF of 4 and 5 or 5 and 6 is 1.

(b) The HCF of two consecutive even numbers is 2.

For example: HCF of 2 and 4 or 4 and 6 is 2.

(c) The HCF of two consecutive odd numbers is 1.

For example: HCF of 5 and 7 or 7 and 9 is 1.

 

3. HCF of co-prime numbers 4 and 15 was found as follows by factorisation : 4 = 2 × 2 and 15 = 3 × 5 since there is no common prime factor, so HCF of 4 and 15 is 0. Is the answer correct? If not, what is the correct HCF?

Solution: No, the answer is incorrect. The correct HCF is 1.

 

Answer:


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