How many factors of 1080are perfect squares?a)6b)4c)8d)12Correct answer is option 'B'. Can you explain this answer?

Question

Answer

The factors of 1080 which are perfect square:

1080 → 2³ × 3³ × 5

For, a number to be a perfect square, all the powers of numbers should be even number.

Power of 2 → 0 or 2
Power of 3 → 0 or 2
Power of 5 → 0

So, the factors which are perfect square are 1, 4, 9, 36.
Hence, Option B is correct.

Answer

If the question is like to find how many factors are perfect square of any number ..

step 1 -the very first step is to prime factorize it by hcf method or lcm method
eg.. here it is 1080
so we get 2×2×2 = 2³
5 = 5¹
3×3×3 = 3³

step 2- find the number of even number in the power considering 0 as a even number too
2³ = till 3 there are two (2) even numbers I. e 0,2
5¹= till 1 there are one (1) even number I. e 0
3³= till 3 there are two(2) even number i. e 0,2

step 3 - multiply the number of even numbers
2×1×2= 4 = and here is your answer

Answer

Answer

Solution:
Prime factorize 1080 as $2^3\cdot3^3\cdot5$.

A perfect square will have only even exponents of its prime factors.

Number of factors of 1080:

- $(3+1)\cdot(3+1)\cdot(1+1) = 64$ factors

Number of factors of 1080 that are perfect squares:

- $2\cdot2\cdot1 = 4$ factors

Therefore, the correct answer is option (B).

Answer

How to find all the 32 factors of 1080?

Answer

How one can find all the factors of 1080

Answer

Can you give esyest method of making factors of big number

Answer

Solution:

To find the factors of 1080, we use prime factorization.

Prime factorization of 1080:

1080 = 2^3 × 3^3 × 5

To find the factors of 1080, we can list out all possible combinations of the prime factors:

Factors of 1080:

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 135, 180, 270, 540, 1080

To find the perfect square factors of 1080, we need to find the factors that can be written as the square of an integer.

Perfect square factors of 1080:

1, 4, 9, 36

Therefore, there are 4 perfect square factors of 1080.

Hence, the correct answer is option B.

Answer

4

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