CBSE Class 6 Mathematics Playing with Numbers Assignments Set 09

Question. What are Co-primes? Write at least 5 pairs of Co-prime nos. Are Co-primes always prime? If no, give an example.
Answer: Two numbers having only \( 1 \) as a common factor are called co-prime numbers.
Five pairs of co-prime numbers: \( (2,3), (3,4), (4,5), (5,6), (6,7) \).
No, co-primes are not always prime. For example, \( (8,9) \) is a pair of co-prime numbers, but neither \( 8 \) nor \( 9 \) is a prime number.

Question. Express 36 and 84 as Sum of two odd primes.
Answer:
\( 36 = 7 + 29 \)
\( 84 = 41 + 43 \)

Question. Can you find an even number greater than 4 which cannot be expressed as a sum of two odd primes?
Answer: No

Question. Write True (T) or False (F)
(i) one is the smallest prime number
(ii) Prime number is always odd no.
(iii) The sum of two prime nos. is always a prime number.
(iv) If two numbers are Co-prime, at least one of them must be a prime number.
Answer:
(i) False (F)
(ii) False (F)
(iii) False (F)
(iv) False (F)

Question. List the prime number having 5 as the units digit.
Answer: \( 5 \)

Question. Express 100 as the Sum of two primes in different ways.
Answer:
\( 100 = 3 + 97 \)
\( 100 = 11 + 89 \)
\( 100 = 17 + 83 \)
\( 100 = 29 + 71 \)
\( 100 = 41 + 59 \)
\( 100 = 47 + 53 \)

Question. List the first eight even numbers which can be expressed as the Sum of twin primes.
Answer:
\( 8 = 3 + 5 \)
\( 12 = 5 + 7 \)
\( 24 = 11 + 13 \)
\( 36 = 17 + 19 \)
\( 60 = 29 + 31 \)
\( 84 = 41 + 43 \)
\( 120 = 59 + 61 \)
\( 144 = 71 + 73 \)

Question. List all such pairs of primes upto 100 whose difference is (i) 1 (ii) 3
Answer:
(i) \( (2, 3) \)
(ii) \( (2, 5) \)

Question. Both 17 and 71 are primes. List all other pairs of two digit primes which have the same digits. Name such type of primes.
Answer: Pairs of two digit primes with the same digits: \( (13, 31) \), \( (37, 73) \), and \( (79, 97) \).
Such primes are called reversible primes (or emirps).

Question. Find all factors of 496. Is it a perfect number?
Answer: Factors of \( 496 \) are: \( 1, 2, 4, 8, 16, 31, 62, 124, 248, \text{ and } 496 \).
Yes, it is a perfect number because the sum of its proper factors is equal to the number itself: \( 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496 \).