Number of ways in which a composite number N can be resolved into two factors, which are prime to each other if N is of the form 22 32 52 72, is

Question

Number of ways in which a composite number N can be resolved into two factors, which are prime to each other if N is of the form 22 32 52 72, is (A) 2 (B) 22 (C) 24 (D) 23

Tardigrade Admin · Accepted Answer

Here co-prime numbers are 2, 3, 5, 7 Counted prime numbers = 4 (Fact) The number of ways in which a composite number N can be broken into two factors, which are prime to each other is 2n - 1. ∴ Required number of ways = 2n- 1 = 24 - 1 = 23 = 8

Q. Number of ways in which a composite number $N$ can be resolved into two factors, which are prime to each other if $N$ is of the form $2^{2} 3^{2} 5^{2} 7^{2}$ , is

$2$

$2^{2}$

$2^{4}$

$2^{3}$

Here co-prime numbers are $2, 3, 5, 7$
Counted prime numbers $= 4$
(Fact) The number of ways in which a composite number $N$ can be broken into two factors, which are prime to each other is $2^{n - 1}$ .
$∴$ Required number of ways $= 2^{n - 1}$
$= 2^{4 - 1} = 2^{3} = 8$

Q. Number of ways in which a composite number N can be resolved into two factors, which are prime to each other if N is of the form 22325272, is

2

22

24

23

Here co-prime numbers are 2,3,5,7 Counted prime numbers =4 (Fact) The number of ways in which a composite number N can be broken into two factors, which are prime to each other is 2n−1. ∴ Required number of ways =2n−1 =24−1=23=8

Q. Number of ways in which a composite number $N$ can be resolved into two factors, which are prime to each other if $N$ is of the form $2^{2} 3^{2} 5^{2} 7^{2}$ , is

$2$

$2^{2}$

$2^{4}$

$2^{3}$

Here co-prime numbers are $2, 3, 5, 7$
Counted prime numbers $= 4$
(Fact) The number of ways in which a composite number $N$ can be broken into two factors, which are prime to each other is $2^{n - 1}$ .
$∴$ Required number of ways $= 2^{n - 1}$
$= 2^{4 - 1} = 2^{3} = 8$