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12. Write all the factors of 30 which are not the factors of 12.
13. Write the odd factors of 240.
14. Show that 496 is a perfect number.
15. Write all the primes less than 100.
16. Write all pairs of twin primes less than 100.
17 Express 121 as the sum of eleven odd numbers.
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1.
d) 3
d) 120
a) 5
d) 36
The difference between successor and predecessor of any number is
a) o
b) 1
c) 2
2. The sum of successors of the first five natural numbers is
b) 20
c) 25
3. The sum of successor of 18 and predecessor of 18 is
a) 2
b) 19
c) 17
4. Among the following, a prime number is
a) 91
b) 41
c) 81
A natural number which is even prime is
a) 1
b) 2.
c)3
d) 51
d) 4
Answers
Step-by-step explanation:
12. 30 is a composite number. 30 = 1 x 30, 2 x 15, 3 x 10, or 5 x 6. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Prime factorization: 30 = 2 x 3 x 5.
13. 240 is a composite number.
Prime factorization: 240 = 2 x 2 x 2 x 2 x 3 x 5, which can be written 2⁴ x 3 x 5.
The exponents in the prime factorization are 4, 1 and 1. ...
Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.
14. Yes, 496 is a perfect number, that is to day 496 equals the sum of its proper positive divisors, i.e., the sum of its divisors excluding 496 itself. Indeed, 496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248.
15. The first 25 prime numbers (all the prime numbers less than 100) are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
16. The twin primes between 1 and 100 are; (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).
17. 121 = 1+3+5+7+9+11+13+15+17+19+21.
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