Question

Define HCF of two positive integers and find the HCF of the following pairs of numbers:
(i) 32 and 54 (ii) 18 and 24
(iii) 70 and 30 (iv) 56 and 88
(v) 475 and 495 (vi) 75 and 243
(vii)240 and 6552(viii)155 and 1385
(ix) 100 and 190 (x) 105 and 120

Answer 1

HCF - Highest Common Factor

A common factor of two or more numbers that too largest among the remaining factors is called the highest common factor.

(i) 32 and 54

The factors of 32 are: 1, 2, 4, 8, 16, 32

The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54

Then the greatest common factor is 2.

(ii) 18 and 24

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

Then the greatest common factor is 6.

(iii) 70 and 30

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

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

Then the greatest common factor is 10.

(iv) 56 and 88

The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56

The factors of 88 are: 1, 2, 4, 8, 11, 22, 44, 88

Then the greatest common factor is 8.

(v) 475 and 495

The factors of 475 are: 1, 5, 19, 25, 95, 475

The factors of 495 are: 1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, 495

Then the greatest common factor is 5.

(vi) 75 and 243

The factors of 75 are: 1, 3, 5, 15, 25, 75

The factors of 243 are: 1, 3, 9, 27, 81, 243

Then the greatest common factor is 3.

(vii)240 and 6552

The factors of 240 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240

The factors of 6552 are: 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 18, 21, 24, 26, 28, 36, 39, 42, 52, 56, 63, 72, 78, 84, 91, 104, 117, 126, 156, 168, 182, 234, 252, 273, 312, 364, 468, 504, 546, 728, 819, 936, 1092, 1638, 2184, 3276, 6552

Then the greatest common factor is 24.

(viii)155 and 1385

The factors of 155 are: 1, 5, 31, 155

The factors of 1385 are: 1, 5, 277, 1385

Then the greatest common factor is 5.

(ix) 100 and 190

The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100

The factors of 190 are: 1, 2, 5, 10, 19, 38, 95, 190

Then the greatest common factor is 10.

(x) 105 and 120

The factors of 105 are: 1, 3, 5, 7, 15, 21, 35, 105

The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Then the greatest common factor is 15.

Answer 2

Step-by-step explanation:

The HCF of the following pairs of numbers:-

(i) 32 = 2×2×2×2×2

   54 = 2×3×3×3

   So highest common factor = 2

(ii) 18 = 2×3×3

    24 = 2×2×2×3

    So highest common factor = 2×3 =6

(iii) 70 = 2×5×7

     30 = 2×3×5

     So highest common factor = 2×5 =10

(iv) 56 = 2×2×2×7

     88 = 2×2×2×11

     So highest common factor = 2×2×2 =8

(v)  475 = 5×5×19

     495 = 3×3×5×11

     So highest common factor = 5

(vi) 75 = 3×5×5

     243 = 3×3×3×3×3

     So highest common factor = 3

(vii) 240 = 2×2×2×2×3×5

      6552 = 2×2×2×3×3×7×13

      So highest common factor = 2×2×2×3 =24

(viii) 155 = 5×31

       1385 = 5×277

       So highest common factor = 5

(ix)  100 = 2×2×5×5

      190 =2×5×19

      So highest common factor = 2×5 =10

(x)   105 = 3×5×7

      120 = 2×2×2×3×5

      So highest common factor = 3×5 =15