Question

2. The prime factorization of an even square number is as shown 3 x 3 x 5 x 5 x 7 x 7 x 7 x 2 x p. What is the smallest value of p?

a) 2
b)4
c) 14
d)28​

Answer 1

Answer:

C) 14 is the answer..........

Answer 2

Answer:

The smallest value of p is c) 14

Step-by-step explanation:

In the above question;

Given:

Prime factorisation of an even number- 3×3×5×5×7×7×7×2×p

So, what does Prime factorisation mean?

Prime factorisation is a way to find the prime factors of any given number.

For example: Prime factorisation of 28 will be written as 2×2×7 or 2²×7

where 2 and 7 are prime numbers.

To find:

value of p

Solution:

First, we have to make it into a even square number

For making it an even square number, we need to have pairs of each numbers:

(3x3) x (5x5) x (7x7) x 7 x 2.

Since 7 and 2 are not in pairs, number cannot be even square. So if we have p = 14 or p = 7 x 2,

then we will have :

(3x3) x (5x5) x (7x7) x 7 x 2 x 7 x 2

Rearranging, (3x3) x (5x5) x (7x7) x (7x7) x (2x2)

which is a perfect square.

Hence, the p value must be 14

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