Question

2. If A = {Prime factors of 24} B = {Prime factors of 6} Write down the elements of sets A and B. Hence, state whether the sets A and B are equal
​

Answer 1

Answer:

Factors of 24 are the numbers, which gives the result as 24 when multiplied together in pair. You can also say, if any number divides number 24 and gives no remainder, then it is a factor.

24 is a composite number, therefore it will have factors more than two. 

The prime factorisartion of 24 gives,

24 = 2 x 2 x 2 x 3 = 23 x 3

We can see here, the exponent of 2 is 3 and 3 is 1.

Now, to find the number of factors of 24 we need to add 1 each to the exponents and multiply them, such as:

(3+1) x (1+1)

= 4 x 2

= 8

Hence, there are 8 positive factors for number 24.

In the same way, we can find a list of factors of 36, 12, 18 and other composite numbers. Whereas the prime factors consist of only prime numbers. The multiples of 24 are extended times tables, such as, 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360 and so on. We will find the factors of a number, 24, with the help of the multiplication method.