Question

Find the number of divisors of 1080 excluding the
divisors, which are perfect squares.
the answer is not 30 it's 28. How?
(a) 28
(b) 29
(c) 30
(d) 31​

Answer 1

Answer:

Hey Buddy....!!

Your answer is :

(a) 28

1080 = 2^3 *3^3 *5^1

1080 = 2^3 *3^3 *5^1total no. of divisors = (3+1)*(3+1)*(1+1) = 32

1080 = 2^3 *3^3 *5^1total no. of divisors = (3+1)*(3+1)*(1+1) = 32only 4 divisors 1, 2^2=4 , 3^2=9 & 2^2*3^2=36 are perfect squares

1080 = 2^3 *3^3 *5^1total no. of divisors = (3+1)*(3+1)*(1+1) = 32only 4 divisors 1, 2^2=4 , 3^2=9 & 2^2*3^2=36 are perfect squaresso,number of divisors excluding perfect squares divisors = 32-4 = 28

Answer 2

The answer is option (a) 28

Given number : 1080

To find: Number of divisors of 1080 excluding perfect squares

Solution:

If n is a natural number and n = pᵃ × qᵇ × $r^{c}$ where p, q and r are prime numbers and a, b, c are the powers

Then the total number of divisors of n is given by (a+1)(b+1)(c+1)

Now find number of divisors of 1080 using above formula

write 1080 as product of prime numbers

⇒ 1080 = 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2³× 3³×5  

Therefore, number of divisors of 1080 = (3+1)(3+1)(1+1) = 4 × 4 × 2 = 32

32 divisors of 1080 are  1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30,

36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080.  

The squares among these divisors perfect squares are 1, 4, 9, 36

Number of divisors of 1080 excluding perfect squares = 32 - 4 = 28

Therefore, number of divisors of 1080 excluding perfect squares is 28

#SPJ2