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प्रश्न
The sum of all natural numbers 'n' such that 100 < n < 200 and H.C.F. (91, n) > 1 is ______.
विकल्प
3203
3221
3121
3303
MCQ
रिक्त स्थान भरें
उत्तर
The sum of all natural numbers 'n' such that 100 < n < 200 and H.C.F. (91, n) > 1 is 3121.
Explanation:
91 = 13 × 7 ∴ HCF (91, n) > 1
Sum of n = multiple of 7 + multiple of 13 – multiple of 13 × 7
= (105 + ....... + 196) + (104 + ....... 195) – 182
= 7(105 + 196) + 4(104 + 195) – 182
= 2107 + 1196 – 182
= 3121
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