Question

· In the set of factors of a whole number 'n' including 'n' itself but not 'l' is
denoted by F(n). If F(16) F(40) = F(x) then 'x' is
1) 4
2) 8
3) 6
4) 10
​

Answer 1

The value of F(x) is F(8).

To find : The value of x.

Given :

• In the set of factors of a whole number 'n' including 'n' itself but not '1'.
• Which is denoted by F(n).
• F(16) ∩ F(40) = F(x).

In F(16) the value of n is 16.

In F(40) the value of n is 40.

Finding the factors :

• Factor of 16 = 1, 2, 4, 8, 16
• Factor of 40 = 1, 2, 4, 5, 8, 10, 20, 40

From the given, in the set of factors of a whole number 'n' including 'n' itself but not '1'. So, including 'n' neglecting the value '1'.

We get,

F(16) = {2, 4, 8, 16}

F(40) = {2, 4, 5, 8, 10, 20, 40}

F(16) ∩ F(40) = F(x).

While intersecting we get,

F(16) ∩ F(40) = {2, 4, 8, 16} ∩ {2, 4, 5, 8, 10, 20, 40}

Take the common values from F(16) and F(40),

F(16) ∩ F(40) = {2, 4, 8}

Factor of 8 is 1,2,4,8.

As per the question excluding the value '1', we get 2, 4, 8.

Hence, F(16) ∩ F(40) = {2, 4, 8} = F(8) = F(x)

x = 8

Therefore, the option (2) - 8 is the correct answer.

To learn more...

1. Write any four factors of 16

https://brainly.in/question/6291735

2. Write all the factors of 40.

https://brainly.in/question/5046809

Answer 2

Given, In the set of factors of a whole number 'n' including 'n' itself but not '1' is denoted by F(n).

Finding the Factors of 16 and 40:

• Factors of 16

16 = 1 × 16

= 2 × 8

= 4 × 4

F(16) = { 2,4,8,16 }

• Factors of 40

40 = 1 × 40

= 2 × 20

= 4 × 10

= 5 × 8

F(40) = { 2,4,5,8,10,20,40 }

$F(16) \cap F(40) = F(x)$

$\implies \{ 2,4,8,16\} \cap \{ 2,4,5,8,10,20,40}= F(x)$

$\implies \{2,4,8\} = F(x)$

$\implies F(8) = F(x)$

$\implies 8 = x$

Therefore.,

$Option \: \pink { ( 2 ) } \: is \: correct.$

•••♪