I. Identify Ihe following numbers as prime
or composite.
ia) 13 (b) 27 (c) 32 (d) 2
(e) 39 (!) 63 (a) 98 (n) 99
(!) 35 0) 19 (k) 41 (!) 65
(m) 22 (n) S3 (O) 23 pi 61.
The prime numbers in the given list are:
(a) 13
(d) 2
(!) 19
(!) 41
(!) 61
All the other numbers are composite.
I can help you identify whether each of the given numbers is prime or composite. Here's the breakdown:
a) 13 - Prime
b) 27 - Composite
c) 32 - Composite
d) 2 - Prime
e) 39 - Composite
f) 63 - Composite
g) 98 - Composite
h) 99 - Composite
i) 35 - Composite
j) 19 - Prime
k) 41 - Prime
l) 65 - Composite
m) 22 - Composite
n) 53 - Prime
o) 23 - Prime
p) 61 - Prime
So, here's the list of prime and composite numbers:
Prime: 13, 2, 19, 41, 53, 23, 61
Composite: 27, 32, 39, 63, 98, 99, 35, 65, 22
To identify whether a number is prime or composite, we need to understand the definitions of prime and composite numbers.
- Prime number: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and itself.
- Composite number: A composite number is a positive integer greater than 1 that has at least one positive divisor other than 1 and itself. In other words, a composite number can be divided evenly by numbers other than 1 and itself.
Now, let's go through each number given and identify whether it is prime or composite:
(a) 13: Prime number
To determine this, you can check if any number from 2 to the square root of 13 divides 13 evenly. As there are no divisors for 13 other than 1 and 13, it is a prime number.
(b) 27: Composite number
To determine this, you can check if any number from 2 to the square root of 27 divides 27 evenly. In this case, 3 is a divisor of 27, so it is not a prime number.
(c) 32: Composite number
To determine this, you can check if any number from 2 to the square root of 32 divides 32 evenly. In this case, 2, 4, 8, and 16 are all divisors of 32, so it is not a prime number.
(d) 2: Prime number
By definition, the number 2 is the only even prime number. It is divisible by 1 and 2, and no other numbers, so it is a prime number.
(e) 39: Composite number
To determine this, you can check if any number from 2 to the square root of 39 divides 39 evenly. In this case, 3 is a divisor of 39, so it is not a prime number.
(f) 63: Composite number
To determine this, you can check if any number from 2 to the square root of 63 divides 63 evenly. In this case, 3, 7, and 9 are all divisors of 63, so it is not a prime number.
(g) 98: Composite number
To determine this, you can check if any number from 2 to the square root of 98 divides 98 evenly. In this case, 2, 7, 14, and 49 are all divisors of 98, so it is not a prime number.
(h) 99: Composite number
To determine this, you can check if any number from 2 to the square root of 99 divides 99 evenly. In this case, 3 is a divisor of 99, so it is not a prime number.
(i) 35: Composite number
To determine this, you can check if any number from 2 to the square root of 35 divides 35 evenly. In this case, 5 and 7 are both divisors of 35, so it is not a prime number.
(j) 19: Prime number
To determine this, you can check if any number from 2 to the square root of 19 divides 19 evenly. As there are no divisors for 19 other than 1 and 19, it is a prime number.
(k) 41: Prime number
To determine this, you can check if any number from 2 to the square root of 41 divides 41 evenly. As there are no divisors for 41 other than 1 and 41, it is a prime number.
(l) 65: Composite number
To determine this, you can check if any number from 2 to the square root of 65 divides 65 evenly. In this case, 5 and 13 are both divisors of 65, so it is not a prime number.
(m) 22: Composite number
To determine this, you can check if any number from 2 to the square root of 22 divides 22 evenly. In this case, 2 and 11 are both divisors of 22, so it is not a prime number.
(n) 53: Prime number
To determine this, you can check if any number from 2 to the square root of 53 divides 53 evenly. As there are no divisors for 53 other than 1 and 53, it is a prime number.
(o) 23: Prime number
To determine this, you can check if any number from 2 to the square root of 23 divides 23 evenly. As there are no divisors for 23 other than 1 and 23, it is a prime number.
(p) 61: Prime number
To determine this, you can check if any number from 2 to the square root of 61 divides 61 evenly. As there are no divisors for 61 other than 1 and 61, it is a prime number.
In conclusion, the prime numbers in this list are 13, 2, 19, 41, 53, 23, and 61. The composite numbers in this list are 27, 32, 39, 63, 98, 99, 35, 65, and 22.