Class 8 Exam > Class 8 Questions > Which is a 3-digit numbers, such that all its...
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Which is a 3-digit numbers, such that all its digits are prime and the 3 digits are the factors of the number?
- a)735
- b)537
- c)435
- d)245
Correct answer is option 'A'. Can you explain this answer?
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Which is a 3-digit numbers, such that all its digits are prime and the...
735 is a number having all its digits, a prime number and all the digits of 735 are the factors of 735.
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Which is a 3-digit numbers, such that all its digits are prime and the...
Prime Digits:
To find a 3-digit number such that all its digits are prime, we need to consider the prime numbers less than 10. The prime digits are 2, 3, 5, and 7.
Factors of a Number:
The factors of a number are the numbers that divide the given number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Analysis of Options:
Let's analyze each option and check if all the digits are prime and if the digits are factors of the number.
a) 735:
- All the digits (7, 3, 5) are prime.
- The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735.
- So, all the digits are prime and are factors of the number.
b) 537:
- The digit 7 is prime, but the digits 5 and 3 are not prime.
- So, this option does not satisfy the condition.
c) 435:
- The digits 5 and 3 are prime, but the digit 4 is not prime.
- So, this option does not satisfy the condition.
d) 245:
- The digits 2, 4, and 5 are prime.
- The factors of 245 are 1, 5, 7, 35, 49, 245.
- So, all the digits are prime and are factors of the number.
Conclusion:
Among the given options, only option a) 735 and option d) 245 have all prime digits. But option d) does not have all its digits as factors of the number. Therefore, the correct answer is option a) 735, as it satisfies both conditions of having all prime digits and all digits being factors of the number.
To find a 3-digit number such that all its digits are prime, we need to consider the prime numbers less than 10. The prime digits are 2, 3, 5, and 7.
Factors of a Number:
The factors of a number are the numbers that divide the given number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Analysis of Options:
Let's analyze each option and check if all the digits are prime and if the digits are factors of the number.
a) 735:
- All the digits (7, 3, 5) are prime.
- The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735.
- So, all the digits are prime and are factors of the number.
b) 537:
- The digit 7 is prime, but the digits 5 and 3 are not prime.
- So, this option does not satisfy the condition.
c) 435:
- The digits 5 and 3 are prime, but the digit 4 is not prime.
- So, this option does not satisfy the condition.
d) 245:
- The digits 2, 4, and 5 are prime.
- The factors of 245 are 1, 5, 7, 35, 49, 245.
- So, all the digits are prime and are factors of the number.
Conclusion:
Among the given options, only option a) 735 and option d) 245 have all prime digits. But option d) does not have all its digits as factors of the number. Therefore, the correct answer is option a) 735, as it satisfies both conditions of having all prime digits and all digits being factors of the number.
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Which is a 3-digit numbers, such that all its digits are prime and the...
735
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Which is a 3-digit numbers, such that all its digits are prime and the 3 digits are the factors of the number?a)735b)537c)435d)245Correct answer is option 'A'. Can you explain this answer?
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