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What number am I?
• I am a two-digit even number.
• I am a common multiple of 6 and 7.
• I have a total of 8 factors.
• I am a two-digit even number.
• I am a common multiple of 6 and 7.
• I have a total of 8 factors.
- a)35
- b)42
- c)36
- d)84
Correct answer is option 'B'. Can you explain this answer?
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What number am I?• I am a two-digit even number.• I am a com...
Identifying the Number
To find the number based on the given clues, we will analyze each criterion step-by-step.
1. Two-Digit Even Number
- The number must be between 10 and 99.
- It should be an even number, meaning it ends in 0, 2, 4, 6, or 8.
2. Common Multiple of 6 and 7
- The least common multiple (LCM) of 6 and 7 can be calculated:
- LCM(6, 7) = 42
- Therefore, any common multiple of 6 and 7 must be a multiple of 42 (e.g., 42, 84, etc.).
3. Total of 8 Factors
- To determine the number of factors, we can factorize the number into its prime components.
- A number has 8 factors if it can be represented in the form:
- p^7 (1 prime raised to the power of 7)
- p^3 * q (2 different primes, one raised to 3)
- p^1 * q^1 * r^1 (3 different primes)
Analysis of Options
- a) 35: Factors are 1, 5, 7, 35 (4 factors)
- b) 42: Factors are 1, 2, 3, 6, 7, 14, 21, 42 (8 factors)
- c) 36: Factors are 1, 2, 3, 4, 6, 9, 12, 18, 36 (9 factors)
- d) 84: Factors are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 (12 factors)
Conclusion
- The only number that meets all the criteria is 42:
- It is even.
- It is a common multiple of 6 and 7.
- It has exactly 8 factors.
Thus, the correct answer is option 'B' (42).
To find the number based on the given clues, we will analyze each criterion step-by-step.
1. Two-Digit Even Number
- The number must be between 10 and 99.
- It should be an even number, meaning it ends in 0, 2, 4, 6, or 8.
2. Common Multiple of 6 and 7
- The least common multiple (LCM) of 6 and 7 can be calculated:
- LCM(6, 7) = 42
- Therefore, any common multiple of 6 and 7 must be a multiple of 42 (e.g., 42, 84, etc.).
3. Total of 8 Factors
- To determine the number of factors, we can factorize the number into its prime components.
- A number has 8 factors if it can be represented in the form:
- p^7 (1 prime raised to the power of 7)
- p^3 * q (2 different primes, one raised to 3)
- p^1 * q^1 * r^1 (3 different primes)
Analysis of Options
- a) 35: Factors are 1, 5, 7, 35 (4 factors)
- b) 42: Factors are 1, 2, 3, 6, 7, 14, 21, 42 (8 factors)
- c) 36: Factors are 1, 2, 3, 4, 6, 9, 12, 18, 36 (9 factors)
- d) 84: Factors are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 (12 factors)
Conclusion
- The only number that meets all the criteria is 42:
- It is even.
- It is a common multiple of 6 and 7.
- It has exactly 8 factors.
Thus, the correct answer is option 'B' (42).
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What number am I?• I am a two-digit even number.• I am a com...
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What number am I?• I am a two-digit even number.• I am a common multiple of 6 and 7.• I have a total of 8 factors.a)35b)42c)36d)84Correct answer is option 'B'. Can you explain this answer?
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