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The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
- a)9000
- b)9400
- c)9600
- d)9800
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The greatest number of four digits which is divisible by 15, 25, 40 an...
Greatest number of 4−digits is 9999.
Now, 15=3×5
25 = 5×5
40 = 2×2×2×5
and 75 = 3×5×5
L.C.M. of 15,25,40 and 75 is 2×2×2×3×5×5 = 600.
On dividing 9999 by 600, the remainder is 399.
Required number = (9999−399) = 9600.
Most Upvoted Answer
The greatest number of four digits which is divisible by 15, 25, 40 an...
To find the greatest number of four digits that is divisible by 15, 25, 40, and 75, we need to find the least common multiple (LCM) of these numbers.
Finding the LCM:
1. Prime factorize each number:
- 15 = 3 × 5
- 25 = 5 × 5
- 40 = 2 × 2 × 2 × 5
- 75 = 3 × 5 × 5
2. Identify the highest power of each prime factor:
- 3 occurs once
- 5 occurs twice
- 2 occurs three times
3. Multiply these prime factors together:
LCM = 3 × 5 × 5 × 2 × 2 × 2 = 600
Finding the greatest number of four digits divisible by 600:
To find the greatest number of four digits divisible by 600, we need to find the largest multiple of 600 that is less than 10,000.
Divide 10,000 by 600:
10,000 ÷ 600 = 16 remainder 400
Subtract the remainder from 10,000:
10,000 - 400 = 9,600
Therefore, the greatest number of four digits divisible by 15, 25, 40, and 75 is 9600 (option C).
Finding the LCM:
1. Prime factorize each number:
- 15 = 3 × 5
- 25 = 5 × 5
- 40 = 2 × 2 × 2 × 5
- 75 = 3 × 5 × 5
2. Identify the highest power of each prime factor:
- 3 occurs once
- 5 occurs twice
- 2 occurs three times
3. Multiply these prime factors together:
LCM = 3 × 5 × 5 × 2 × 2 × 2 = 600
Finding the greatest number of four digits divisible by 600:
To find the greatest number of four digits divisible by 600, we need to find the largest multiple of 600 that is less than 10,000.
Divide 10,000 by 600:
10,000 ÷ 600 = 16 remainder 400
Subtract the remainder from 10,000:
10,000 - 400 = 9,600
Therefore, the greatest number of four digits divisible by 15, 25, 40, and 75 is 9600 (option C).
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The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:a)9000b)9400c)9600d)9800Correct answer is option 'C'. Can you explain this answer?
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