The greatest number, which when subtracted from 5834, gives a number exactly…
2024
The greatest number, which when subtracted from 5834, gives a number exactly divisible by 20, 28, 32 and 35 is
Answer: B. 4714 — The required number, when subtracted from 5834, should leave a number exactly divisible by 20, 28, 32, and 35. Therefore, the remainder obtained after…
- A.
1234
- B.
4714
- C.
5678
- D.
9876
Attempted by 10 students.
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Correct answer: B
The required number, when subtracted from 5834, should leave a number exactly divisible by 20, 28, 32, and 35.
Therefore, the remainder obtained after subtraction must be a common multiple of these numbers. To get the greatest number to be subtracted, we should leave the smallest common multiple, i.e., the LCM.
Prime factorization:
20 = 2² × 5
28 = 2² × 7
32 = 2⁵
35 = 5 × 7
LCM = 2⁵ × 5 × 7 = 1120
Now subtract this from 5834:
Required number = 5834 − 1120 = 4714
Hence, the correct answer is Option B (4714).