Exercise 3.2
(1) Write all the factors of the following numbers:
i. 36 ii. 23 iii. 96 iv. 115
(i) 36
Factors of 36 are :
1 ×
2 ×
3 ×
6 ×
Therefore, factors of 36 are
(ii) 23
Factors of 23 are:
Since 23 is a prime number, it has only two factors: 1 and 23.
Therefore, the factors of 23 are
(iii) 96
Factors of 96 are:
1 ×
3 ×
4 ×
8 ×
Therefore, the factors of 96 are
(iv) 115
Factors of 115 are:
1 ×
5 ×
Therefore, the factors of 115 are
2. Which of the following pairs are co-prime?
a. 18 and 35 b. 216 and 215
c. 30 and 415 d. 17 and 68
We will be using the concept of co-prime numbers to solve this.
(a) Given numbers are 18 and 35
Factors of 18 are
Factors of 35 are
The common factor of 18 and 35 is only
Therefore, 18 and 35 are
(b) Given numbers are 15 and 37
Factors of 15 are
Factors of 37 are
The common factor of 15 and 37 is only
Therefore, 15 and 37 are
(c) Given numbers are 30 and 415
Factors of 30 are
Factors of 415 are
The common factors of 30 and 415 are
Therefore, 30 and 415
(d) Given numbers are 17 and 68
Factors of 17 are
Factors of 68 are
The common factors of 17 and 68 are
Therefore, 17 and 68
(e) Given numbers are 216 and 215
Factors of 216 are
Factors of 215 are
The common factor of 216 and 215 is only
Therefore, 216 and 215
(f) Given numbers are 81 and 16
Factors of 81 are
Factors of 16 are
The common factor of 81 and 16 is only
Therefore, 81 and 16
3. What is the greatest prime number between 1 and 20?
The prime numbers between 1 and 20 are:
The greatest prime number in this range is
4. Find the prime and composite numbers between 10 and 30?
we have to find the prime numbers that are between 10 and 30. So here it is well known that the prime numbers have just two factors. The two factors are the number one and the number itself.
So, we will start with the number 10, and we see that it has three factors, i.e.,
Next, 11 has just two factors, i.e.,
Next, 12 has the following factors, i.e.,
Next, 13 has just two factors, i.e.,
Next, 14 has the following factors, i.e.,
Next, 15 has the following factors, i.e.,
Next, 16 has the following factors, i.e.,
Next, 17 has just two factors, i.e.,
Next, 18 has the following factors, i.e.,
Next, 19 has just two factors, i.e.,
Next, 20 has the following factors, i.e.,
Next, 21 has the following factors, i.e.,
Next, 22 has the following factors, i.e.,
Next, 23 has just two factors, i.e.,
Next, 24 has the following factors, i.e.,
Next, 25 has the following factors, i.e.,
Next, 26 has the following factors, i.e.,
Next, 27 has the following factors, i.e.,
Next, 28 has the following factors, i.e.,
Next, 29 has just two factors, i.e.,
Next, 30 has the following factors, i.e.,
Hence, the prime numbers between 10 and 30 are
So, total there are
5. The numbers 17 and 71 are prime numbers. Both these numbers have same digits 1 and 7. Find 2 more such pairs of prime numbers below 100?
We will be using the concepts of prime number to solve this.
The prime numbers between 1 to 100 are
The required pairs of prime numbers(up to 100) having the same digits as 13 and 31 are:
(a) 17 and
(b) 37 and
(c)
6. Write three pairs of twin primes below 20?
Twin primes are pairs of prime numbers that differ by
Three pairs of twin primes below 20 are:
(
(
(
7. Write two prime numbers whose product is 35?
Two prime numbers whose product is 35 are:
8. Express 36 as the sum of two odd primes?
To express 36 as the sum of two odd prime numbers, let's check possible pairs:
9. Write seven consecutive composite numbers less than 100.
Seven consecutive composite numbers (numbers that are not prime) less than 100 are:
10. Express 53 as the sum of three primes?
We will be using the concepts of odd numbers and prime numbers to solve this.
53 can be expressed as
11. Write two prime numbers whose difference is 10?
Two prime numbers whose difference is 10 are:
12. Write three pairs of prime numbers less than 20 whose sum is divisible by 5?
The prime numbers less than 20 are 2, 3, 5, 7, 11, 13, and 17.
We need to form pairs such that the sum of the above prime numbers is divisible by 5.
For a number to be divisible by 5, the last digit of the number should be either
The sum of the prime numbers
The sum of the prime numbers 3 and
The sum of the prime numbers
The sum of the prime numbers 3 and
The sum of the prime numbers 13 and
The sum of the prime numbers 2 and
Hence, the pairs are (