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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?
Verified Answer
The greatest number of four digits which is divisible by 15, 25, 40 an...
Greatest number of 4-digits is 9999.
and L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number=(9999 –399) = 9600.
and L.C.M. of 15, 25, 40 and 75 is 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...
Problem:
The greatest number of four digits which is divisible by 15, 25, 40, and 75.
Solution:
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.
Step 1: Prime Factorization
We start by finding the prime factorization of each number:
- 15 = 3 x 5
- 25 = 5 x 5
- 40 = 2 x 2 x 2 x 5
- 75 = 3 x 5 x 5
Step 2: LCM
The LCM is the product of the highest powers of all the prime factors. We take the highest power of each prime factor from the prime factorization of each number:
- 2^3 x 3^1 x 5^2 = 8 x 3 x 25 = 600
Step 3: Four-digit Number
To find the greatest number of four digits divisible by 15, 25, 40, and 75, we need to find the largest multiple of 600 that is less than 10,000 (the largest four-digit number).
Dividing 10,000 by 600, we get:
- 10,000 ÷ 600 = 16 remainder 400
So, the largest multiple of 600 less than 10,000 is 600 x 16 = 9,600.
Therefore, the greatest number of four digits that is divisible by 15, 25, 40, and 75 is 9,600.
Answer:
The correct answer is option 'C' - 9600.
The greatest number of four digits which is divisible by 15, 25, 40, and 75.
Solution:
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.
Step 1: Prime Factorization
We start by finding the prime factorization of each number:
- 15 = 3 x 5
- 25 = 5 x 5
- 40 = 2 x 2 x 2 x 5
- 75 = 3 x 5 x 5
Step 2: LCM
The LCM is the product of the highest powers of all the prime factors. We take the highest power of each prime factor from the prime factorization of each number:
- 2^3 x 3^1 x 5^2 = 8 x 3 x 25 = 600
Step 3: Four-digit Number
To find the greatest number of four digits divisible by 15, 25, 40, and 75, we need to find the largest multiple of 600 that is less than 10,000 (the largest four-digit number).
Dividing 10,000 by 600, we get:
- 10,000 ÷ 600 = 16 remainder 400
So, the largest multiple of 600 less than 10,000 is 600 x 16 = 9,600.
Therefore, the greatest number of four digits that is divisible by 15, 25, 40, and 75 is 9,600.
Answer:
The correct answer is option 'C' - 9600.
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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? for Class 5 2025 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about 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? covers all topics & solutions for Class 5 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for Class 5 2025 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about 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? covers all topics & solutions for Class 5 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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