Q-1 Find the largest number of five digits which, when divided by 16, 24, 30 or 36, leaves the same remainder 10 in each case.
Solution:
Largest number of 5 digits = 99999.
L.C.M. of 16, 24, 30 and 36 = 720.
On dividing 99999 by 720, remainder obtained is 639.
Hence Largest number of 5 digits divisible by 16, 24, 30 and 36 = (99999 – 639) = 99360.
Hence, required number = (99360 + 10) = 99370.
Q-2 Find the largest number of four digits which, when divided by 10, 20, 30 or 40, leaves the same remainder 5 in each case.
चार अंकों की सबसे बड़ी संख्या ज्ञात कीजिए जिसे 10, 20, 30 या 40 से विभाजित करने पर प्रत्येक स्थिति में समान शेषफल 5 प्राप्त होता है।
Solution:
Largest number of 4 digits = 9999.
L.C.M. of 10, 20, 30 or 40 = 120.
On dividing 9999 by 120, remainder obtained is 39.
Hence Largest number of 4 digits divisible by 10, 20, 30 and 40 = (9999 – 39) = 9960.
Hence, required number = (9960 + 5) = 9965.
Q-3 Find the largest number of three digits which, when divided by 3, 4, 5 or 6, leaves the same remainder 2 in each case.
तीन अंकों की सबसे बड़ी संख्या ज्ञात कीजिए जिसे 3, 4, 5 या 6 से विभाजित करने पर प्रत्येक स्थिति में समान शेषफल 2 प्राप्त होता है।
Solution:
Largest number of 3 digits = 999.
L.C.M. of 3, 4, 5 or 6 = 60.
On dividing 999 by 60, remainder obtained is 39.
Hence Largest number of 3 digits divisible by 3, 4, 5 and 6 = (999 – 39) = 960.
Hence, required number = (960 + 2) = 962.
PRACTICE QUESTIONS
1. Find the largest number of five digits which, when divided by 15, 20, 30 or 35, leaves the same remainder 7 in each case.
2.Find the largest number of four digits which, when divided by 12, 18, 30 or 35, leaves the same remainder 3 in each case.
चार अंकों की सबसे बड़ी संख्या ज्ञात कीजिए जिसे 12, 18, 30 या 35 से विभाजित करने पर प्रत्येक स्थिति में समान शेषफल 5 प्राप्त होता है।
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