Q) A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.

Observe the following factor tree and answer the following:

1. What will be the value of x?
a) 15005              b) 13915                 c) 56920                    d) 17429

2. What will be the value of y?
a) 23                    b) 22                       c) 11                           d) 19

3. What will be the value of z?
a) 22                    b) 23                      c) 17                          d) 19

4. According to Fundamental Theorem of Arithmetic 13915 is a
a) Composite number                         b) Prime number
c) Neither prime nor composite         d) Even number

5. The prime factorisation of 13915 is
a) 5 x 11³ x 13²             b) 5 x 11³ x 23²            c) 5 x 11² x 23                  d) 5 x 11² x 13²  

Ans:

STEP BY STEP SOLUTION

1. Value of X?

Here, As we can see X has two factors of 5 and 2783

We know that number is the product of its factors.

∴ Number X = 5 x 2783

∴ Number X = 13915

Therefore, option b) is correct

2. Value of Y:  

Again we see that 2783 has factors of Y and 253

∴ 2783 = Number Y x 253

∴ Number Y =

∴ Number Y = 11

Therefore, option c) is correct

3. Value of Z:

we see that 253 has factors of 11 and Z

∴ 253 = 11 x Number Z

∴ Number Z =

∴ Number Y = 23

Therefore, option b) is correct

4. Define 13915:

According to the fundamental theorem of arithmetic, every composite number can be factorized as a product of primes.

As seen above, 13915 has factors of 5, 11, 23.

Since this number has more than the two factors (1 and the number itself), hence it is a composite number.

Therefore, option a) is correct

5. Expression for 108: 

By Prime factorisation method, we write:

13915 = 5 x 11 x 11 x 23

∴ 108 = 5 x 11² x 23

Therefore, option c) is correct

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