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
Answers
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.
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