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Which greatest number of 4 digits is exactly divisible by 12, 16, 28 & 36?
- a)6072
- b)8072
- c)8972
- d)9072
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Which greatest number of 4 digits is exactly divisible by 12, 16, 28 &...
Here is the answer.
LCM of 12, 16, 24, 28 and 36
12= 3x2x2
16=2x2x2x2
24=2x2x2x3
28=2x2x7
36=2x2x3x3
so, LCM is 2x2x2x2x3x3x7= 1008
And the greatest 4-digit no. is 9999
so, dividing 9999 by 1008 we get, 9 as quotient and 927 as reminder .
So, the largest 4-digit no. divisible by all these nos. is 9999-927= 9072.
Most Upvoted Answer
Which greatest number of 4 digits is exactly divisible by 12, 16, 28 &...
We need to find the LCM (Least Common Multiple) of 12, 16, and 28.
Prime factorizing these numbers:
12 = 2^2 * 3
16 = 2^4
28 = 2^2 * 7
To find the LCM, we need to take the highest power of each prime factor that appears in any of the numbers.
LCM = 2^4 * 3 * 7 = 336
Now we need to find the greatest number of 4 digits (i.e. less than 10,000) that is divisible by 336.
We can divide 10,000 by 336 to get an estimate:
10,000 ÷ 336 ≈ 29.76
So the highest multiple of 336 that is less than 10,000 is 29 * 336 = 9744.
Therefore, the greatest number of 4 digits that is exactly divisible by 12, 16, and 28 is 9744.
Prime factorizing these numbers:
12 = 2^2 * 3
16 = 2^4
28 = 2^2 * 7
To find the LCM, we need to take the highest power of each prime factor that appears in any of the numbers.
LCM = 2^4 * 3 * 7 = 336
Now we need to find the greatest number of 4 digits (i.e. less than 10,000) that is divisible by 336.
We can divide 10,000 by 336 to get an estimate:
10,000 ÷ 336 ≈ 29.76
So the highest multiple of 336 that is less than 10,000 is 29 * 336 = 9744.
Therefore, the greatest number of 4 digits that is exactly divisible by 12, 16, and 28 is 9744.
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Which greatest number of 4 digits is exactly divisible by 12, 16, 28 &...
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Which greatest number of 4 digits is exactly divisible by 12, 16, 28 & 36?a)6072b)8072c)8972d)9072Correct answer is option 'D'. Can you explain this answer? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Which greatest number of 4 digits is exactly divisible by 12, 16, 28 & 36?a)6072b)8072c)8972d)9072Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which greatest number of 4 digits is exactly divisible by 12, 16, 28 & 36?a)6072b)8072c)8972d)9072Correct answer is option 'D'. Can you explain this answer?.
Which greatest number of 4 digits is exactly divisible by 12, 16, 28 & 36?a)6072b)8072c)8972d)9072Correct answer is option 'D'. Can you explain this answer? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Which greatest number of 4 digits is exactly divisible by 12, 16, 28 & 36?a)6072b)8072c)8972d)9072Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which greatest number of 4 digits is exactly divisible by 12, 16, 28 & 36?a)6072b)8072c)8972d)9072Correct answer is option 'D'. Can you explain this answer?.
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