Question

N= 12^3 x 13^2 x 14. Total number of factors of N is
(a) 64
(6) 192
(c) 24
(d) None of these​

Answer 1

The correct answer would be (d) None of these.

Explanation:

To find the total number of factors of N, we need to consider the prime factorization of N.

Given that N = 12³ x 13² x 14, we can rewrite it as N = (2² x 3)³ x 13² x (2 x 7).

To find the number of factors, we can use the formula:

Number of factors = (a+1)(b+1)(c+1) ... where a, b, c are the exponents of the prime factors.

In this case, the prime factorization of N can be written as $2^{6}$ x 3³ x $7^{1}$ x 13².

Therefore, the number of factors of N would be (6+1)(3+1)(1+1)(2+1) = 7 x 4 x 2 x 3 = 168.

Since none of the given options match the calculated value of 168, the correct answer would be (d) None of these.

For more such questions on prime factorization:

https://brainly.in/question/49326294

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