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The number of 3-digit numbers divisible by 6, is …………...
- a)149
- b)166
- c)150
- d)151
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The number of 3-digit numbers divisible by 6, is ……&hell...
- Smallest 3-digit number divisible by 6:
Start from 100. The smallest number divisible by 6 is 102. - Largest 3-digit number divisible by 6:
Start from 999. The largest number divisible by 6 is 996. - Find how many numbers are in this sequence:
Use the formula for how many multiples exist between two numbers: - Answer: option (c) 150
Community Answer
The number of 3-digit numbers divisible by 6, is ……&hell...
Understanding Divisibility by 6
To determine how many 3-digit numbers are divisible by 6, we need to recall that a number is divisible by 6 if it is divisible by both 2 and 3.
Step 1: Identify the Range of 3-Digit Numbers
- The smallest 3-digit number is 100.
- The largest 3-digit number is 999.
Step 2: Find the First and Last 3-Digit Numbers Divisible by 6
- First 3-digit number divisible by 6:
- Start from 100.
- Check 100 ÷ 6 = 16.67, so the first multiple is 6 * 17 = 102.
- Last 3-digit number divisible by 6:
- Start from 999.
- Check 999 ÷ 6 = 166.5, so the last multiple is 6 * 166 = 996.
Step 3: Calculate the Number of Terms in the Sequence
- The 3-digit numbers divisible by 6 form an arithmetic sequence: 102, 108, ..., 996.
- The first term (a) is 102, the last term (l) is 996, and the common difference (d) is 6.
Step 4: Use the Formula for the Number of Terms
- The formula for the number of terms (n) in an arithmetic sequence is:
n = (l - a) / d + 1
- Plugging in the values:
n = (996 - 102) / 6 + 1
n = 894 / 6 + 1
n = 149 + 1
n = 150
Conclusion
Thus, the total number of 3-digit numbers that are divisible by 6 is 150. Hence, the correct answer is option 'C'.
To determine how many 3-digit numbers are divisible by 6, we need to recall that a number is divisible by 6 if it is divisible by both 2 and 3.
Step 1: Identify the Range of 3-Digit Numbers
- The smallest 3-digit number is 100.
- The largest 3-digit number is 999.
Step 2: Find the First and Last 3-Digit Numbers Divisible by 6
- First 3-digit number divisible by 6:
- Start from 100.
- Check 100 ÷ 6 = 16.67, so the first multiple is 6 * 17 = 102.
- Last 3-digit number divisible by 6:
- Start from 999.
- Check 999 ÷ 6 = 166.5, so the last multiple is 6 * 166 = 996.
Step 3: Calculate the Number of Terms in the Sequence
- The 3-digit numbers divisible by 6 form an arithmetic sequence: 102, 108, ..., 996.
- The first term (a) is 102, the last term (l) is 996, and the common difference (d) is 6.
Step 4: Use the Formula for the Number of Terms
- The formula for the number of terms (n) in an arithmetic sequence is:
n = (l - a) / d + 1
- Plugging in the values:
n = (996 - 102) / 6 + 1
n = 894 / 6 + 1
n = 149 + 1
n = 150
Conclusion
Thus, the total number of 3-digit numbers that are divisible by 6 is 150. Hence, the correct answer is option 'C'.
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The number of 3-digit numbers divisible by 6, is …………...a)149b)166c)150d)151Correct answer is option 'C'. 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 The number of 3-digit numbers divisible by 6, is …………...a)149b)166c)150d)151Correct answer is option 'C'. 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 The number of 3-digit numbers divisible by 6, is …………...a)149b)166c)150d)151Correct answer is option 'C'. Can you explain this answer?.
The number of 3-digit numbers divisible by 6, is …………...a)149b)166c)150d)151Correct answer is option 'C'. 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 The number of 3-digit numbers divisible by 6, is …………...a)149b)166c)150d)151Correct answer is option 'C'. 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 The number of 3-digit numbers divisible by 6, is …………...a)149b)166c)150d)151Correct answer is option 'C'. Can you explain this answer?.
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