Question

Mathematics for Class 6
EXERCISE 2D
method
1. 84. 98
4 72 108. 180
2. 170.238
5. 84. 120. 138
3. 504.980
6. 106. 159. 371
9. 1197, 5320, 4389
Find the HCF of the numbers in each of the following, using the prime factorizatie​

Answer 1

$\large\bf\blue{(1) 84 , 98}$

All the factors of 84 are 2 x 2 x 3 x 7

All the factors of 98 are 2 x 7 x 7

Common factors of 84 and 98 are 2 x 7

Thus, the highest common factor of 84 and 98 is 7

$\large\bf\blue{(2) 72 , 108 , 180}$

All the factors of 72 are 2 x 2 x 2 x 3 x 3

All the factors of 108 are 2 x 2 x 3 x 3 x 3

All the factors of 180 are 2 x 2 x 3 x 3 x 5

Common factors of 72, 108 and 180 are 2 x 2 x 3 x 3

Thus, the highest common factor of 72, 108 and 180 is 3

Hence, HCF of 72, 108 and 180= 3

$\large\bf\blue{(3) 170 , 238}$

All the factors of 170 are 2 x 5 x 17

All the factors of 238 are 2 x 7 x 17

Common factors of 170 and 238 are 2 x 17

Thus, the highest common factor of 170 and 238 is 17

Hence, HCF of 170 and 238= 17

$\large\bf\blue{(4) 84 , 120 , 138}$

All the factors of 84 are 2 x 2 x 3 x 7

All the factors of 120 are 2 x 2 x 2 x 3 x 5

All the factors of 138 are 2 x 3 x 23

Common factors of 84, 120 and 138 are 2 x 3

Thus, the highest common factor of 84, 120 and 138 is 2 x 3

Hence, HCF of 84, 120 and 138= 3

$\large\bf\blue{(5) 504 , 980}$

All the factors of 504 are 2 x 2 x 2 x 3 x 3 x 7

All the factors of 980 are 2 x 2 x 5 x 7 x 7

Common factors of 504 and 980 are 2 x 2 x 7

Thus, the highest common factor of 504 and 980 is 7

Hence, HCF of 504 and 980= 7

$\large\bf\blue{(6) 106 , 159 , 371}$

All the factors of 106 are 2 x 53

All the factors of 159 are 3 x 53

All the factors of 371 are 7 x 53

Common factors of 106, 159 and 371 is 53

Thus, the highest common factor of 106, 159 and 371 is 53

Hence, HCF of 106, 159 and 371= 53

$\large\bf\blue{(7) 1197 , 5320 , 4389}$

All the factors of 1197 are 3 x 3 7 x 19

All the factors of 5320 are 2 x 2 x 2 x 5 x 7 x 19

All the factors of 4389 are 3 x 7 x 11 x 19

Common factors of 1197, 5320 and 4389 are 7 x 19

Thus, the highest common factor of 1197, 5320 and 4389 is 19

Hence, HCF of 1197, 5320 and 4389= 19