Maharashtra Board Class 7 Chapter 3 Set 10 HCF and LCM Solutions

Question 1. Which number is neither a prime number nor a composite number?
Answer: 1
In simple words: The number 1 is unique in number theory; it has only one factor (itself), which means it doesn't fit the definition of a prime number (which has exactly two factors) or a composite number (which has more than two factors).

🎯 Exam Tip: Remember the special case of the number 1; it is neither prime nor composite and is often asked in basic number theory questions.

Question 2. Which of the following are pairs of co-primes?
(i) 8,14
(ii) 4,5
(iii) 17,19
(iv) 27,15
Answer:
(i) Factors of 8: 1, 2, 4, 8
Factors of 14: 1, 2, 7, 14
.. Common factors of 8 and 14: 1,2
.. 8 and 14 are not a pair of co-prime numbers.

(ii) Factors of 4: 1, 4
Factors of 5: 1, 5
.. Common factors of 4 and 5: 1
.. 4 and 5 are a pair of co-prime numbers.

(iii) Factors of 17: 1, 17
Factors of 19: 1, 19
.. Common factors of 17 and 19: 1
.. 17 and 19 are a pair of co-prime numbers.

(iv) Factors of 27: 1, 3, 9, 27
Factors of 15: 1, 3, 5, 15 .
.. Common factors of 27 and 15 : 1,3
.. 27 and 15 are not a pair of co-prime numbers.
In simple words: Co-prime numbers are a pair of numbers that have only 1 as their common factor. We find the factors of each number in the pair and check if 1 is their only common factor.

🎯 Exam Tip: To identify co-prime numbers, always list all factors for each number in the pair. If 1 is the *only* common factor, then they are co-prime.

Question 3. List the prime numbers from 25 to 100 and say how many they are.
Answer: 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
There are 16 prime numbers from 25 to 100.
In simple words: Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. We list all such numbers in the given range.

🎯 Exam Tip: Memorizing common prime numbers up to a certain range can save time. Always double-check your list to ensure no composite numbers are included.

Question 4. Write all the twin prime numbers from 51 to 100.
Answer:
1. 59 and 61
2. 71 and 73
In simple words: Twin prime numbers are pairs of prime numbers that differ by 2. We identify such pairs within the specified range.

🎯 Exam Tip: To find twin primes, first list all prime numbers in the given range, then look for pairs that have a difference of 2.

Question 5. Write 5 pairs of twin prime numbers from 1 to 50.
Answer:
1. 3,5
2. 5,7
3. 11,13
4. 17,19
5. 29,31
6. 41,43
In simple words: Twin primes are prime numbers that are separated by just one even number. We list all such pairs found between 1 and 50.

🎯 Exam Tip: When listing twin primes, ensure both numbers in the pair are indeed prime and their difference is exactly 2. Be careful not to miss any pairs within the given range.

Question 6. Which are the even prime numbers?
Answer: 2
In simple words: An even prime number is a number that is both even (divisible by 2) and prime (only divisible by 1 and itself). The number 2 is the only number that fits this description.

🎯 Exam Tip: The number 2 is a crucial exception in prime numbers as it's the only even prime. All other even numbers are composite.

Maharashtra Board Class 7 Maths Chapter 3 Hcf And Lcm Practice Set 10 Intext Questions And Activities

Question 1. Answer the following questions. (Textbook pg. no. 15)
(i) Which is the smallest prime number?
(ii) List the prime numbers from 1 to 50. How many are they?
(iii) Identify the prime numbers in the list below.
17, 15,4, 3, 1, 2, 12, 23, 27, 35, 41, 43, 58, 51, 72, 79, 91, 97.
Answer:
(i) 2 is the smallest prime number.
(ii) There are 15 prime numbers from 1 to 50.
They are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
(iii) [17], 15,4, [3], 1, [2], 12, [23], 27, 35, [41], [43], 58, 51, 72, [79], 91, [97].
In simple words: This question tests basic knowledge of prime numbers, including identifying the smallest prime, listing primes within a range, and picking primes from a given set of numbers. Remember that 1 is neither prime nor composite.

🎯 Exam Tip: For listing prime numbers, use the Sieve of Eratosthenes method mentally or on paper to accurately identify all primes in the given range. Pay close attention to numbers like 1 and 2, and composite numbers with small factors.