Answer :
Sure! Let's go step-by-step through each question and determine the answers.
### Fill in the Blanks:
1. The only natural number which has exactly one factor is
- The answer is 1, because 1 only has one factor, which is itself.
2. The only prime number which is even is
- The answer is 2, because 2 is the only even number that is prime (divisible only by 1 and itself).
3. The HCF of two co-prime numbers is
- The answer is 1, because co-prime numbers have no common factors other than 1.
4. Two perfect numbers are
- The answer is 6 and 28, because both numbers are equal to the sum of their proper divisors (excluding themselves).
5. The only prime-triplet is
- The answer is 3, 5, and 7, as they are the only set of three consecutive odd numbers that are all prime.
6. The LCM of two or more given numbers is the lowest their common
- The answer is multiple, as LCM stands for Lowest Common Multiple.
7. The HCF of two or more given numbers is the highest of their common
- The answer is factor, as HCF stands for Highest Common Factor.
### True or False Statements:
1. Every natural number has a finite number of factors.
- This statement is True because any natural number has a limited number of divisors.
2. Every natural number has an infinite number of its multiples.
- This statement is True since multiplying a natural number by every integer results in infinitely many multiples.
3. There are infinitely many prime numbers.
- This statement is True, as proven by Euclid's theorem which states that there are infinitely many primes.
4. The HCF of two numbers is smaller than the smaller of the numbers.
- This statement is True because the highest common factor cannot exceed the smallest of the original numbers.
5. The LCM of two numbers is greater than the larger of the numbers.
- This statement is True because the least common multiple is always at least as large as the largest original number.
In summary, the filled responses and true/false answers match:
Fill in the Blanks:
1. 1
2. 2
3. 1
4. 6, 28
5. 3, 5, 7
6. multiple
7. factor
True or False:
1. True
2. True
3. True
4. True
5. True
### Fill in the Blanks:
1. The only natural number which has exactly one factor is
- The answer is 1, because 1 only has one factor, which is itself.
2. The only prime number which is even is
- The answer is 2, because 2 is the only even number that is prime (divisible only by 1 and itself).
3. The HCF of two co-prime numbers is
- The answer is 1, because co-prime numbers have no common factors other than 1.
4. Two perfect numbers are
- The answer is 6 and 28, because both numbers are equal to the sum of their proper divisors (excluding themselves).
5. The only prime-triplet is
- The answer is 3, 5, and 7, as they are the only set of three consecutive odd numbers that are all prime.
6. The LCM of two or more given numbers is the lowest their common
- The answer is multiple, as LCM stands for Lowest Common Multiple.
7. The HCF of two or more given numbers is the highest of their common
- The answer is factor, as HCF stands for Highest Common Factor.
### True or False Statements:
1. Every natural number has a finite number of factors.
- This statement is True because any natural number has a limited number of divisors.
2. Every natural number has an infinite number of its multiples.
- This statement is True since multiplying a natural number by every integer results in infinitely many multiples.
3. There are infinitely many prime numbers.
- This statement is True, as proven by Euclid's theorem which states that there are infinitely many primes.
4. The HCF of two numbers is smaller than the smaller of the numbers.
- This statement is True because the highest common factor cannot exceed the smallest of the original numbers.
5. The LCM of two numbers is greater than the larger of the numbers.
- This statement is True because the least common multiple is always at least as large as the largest original number.
In summary, the filled responses and true/false answers match:
Fill in the Blanks:
1. 1
2. 2
3. 1
4. 6, 28
5. 3, 5, 7
6. multiple
7. factor
True or False:
1. True
2. True
3. True
4. True
5. True
