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How many factors of 10800 are perfect squares?
a)6
b)12
c)8
d)None of these
Correct answer is option 'B'. Can you explain this answer?
b)12
c)8
d)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
How many factors of 10800 are perfect squares?a)6 b)12 c)8 d)None of t...
Prime factorization of 10800 = 24 × 33 × 52
If we prime factorise any number which is a perfect square, we would observe that in all cases the exponent of all the prime factors of the number to be even only.
For example, 36 is perfect square 36 = 22 × 32. Here we can see that the exponent of both 2 and 3 are even.
Again, any factor 10800 will be in the form of 2a × b × 5c.
For the factors to be perfect squares, all the values a, b, and c has to be even only.
Or, the possible values which a can take = 0, 2, 4, i.e. 3 values only. Similarly, b can take 0, 2 i.e. 2 values and c can take 0, 2 i.e. 2 values.
Therefore, the different combinations we can have = 3 x 2 x 2 = 12.
Hence, 10800 has 12 factors which are perfect squares.
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Most Upvoted Answer
How many factors of 10800 are perfect squares?a)6 b)12 c)8 d)None of t...
Answer should be 'd'
bcoz factors of 10800=2^4x 5^2x3^3
2^4=2^0,2^1,2^2,2^3,2^4
similarly, 5^2 =5^0, 5^1,5^2
3^3= 3^0,3^1,3^2, 3^3
and the perfect square -2^0,2^2,2^4,5^0,5^2,3^0,3^2.
no. of factors should be 7....answer is 7
bcoz factors of 10800=2^4x 5^2x3^3
2^4=2^0,2^1,2^2,2^3,2^4
similarly, 5^2 =5^0, 5^1,5^2
3^3= 3^0,3^1,3^2, 3^3
and the perfect square -2^0,2^2,2^4,5^0,5^2,3^0,3^2.
no. of factors should be 7....answer is 7
Community Answer
How many factors of 10800 are perfect squares?a)6 b)12 c)8 d)None of t...
Solution:
To find the factors of 10800, we need to factorize it first.
10800 = 2^3 x 3^3 x 5^2
To be a perfect square, a factor must have all the exponents even.
So, we need to find all possible combinations of 2's, 3's, and 5's.
The total number of factors of 10800 is (3+1) x (3+1) x (2+1) = 96.
Now, we need to count the number of factors that have all the exponents even.
The possible combinations are:
2^0 x 3^0 x 5^0 = 1
2^2 x 3^0 x 5^0 = 4
2^0 x 3^2 x 5^0 = 9
2^0 x 3^0 x 5^2 = 1
2^2 x 3^2 x 5^0 = 36
2^2 x 3^0 x 5^2 = 20
2^0 x 3^2 x 5^2 = 45
2^2 x 3^2 x 5^2 = 180
Therefore, there are a total of 1+4+9+1+36+20+45+180 = 296 factors of 10800 that are perfect squares.
Hence, the correct option is (B) 12.
To find the factors of 10800, we need to factorize it first.
10800 = 2^3 x 3^3 x 5^2
To be a perfect square, a factor must have all the exponents even.
So, we need to find all possible combinations of 2's, 3's, and 5's.
The total number of factors of 10800 is (3+1) x (3+1) x (2+1) = 96.
Now, we need to count the number of factors that have all the exponents even.
The possible combinations are:
2^0 x 3^0 x 5^0 = 1
2^2 x 3^0 x 5^0 = 4
2^0 x 3^2 x 5^0 = 9
2^0 x 3^0 x 5^2 = 1
2^2 x 3^2 x 5^0 = 36
2^2 x 3^0 x 5^2 = 20
2^0 x 3^2 x 5^2 = 45
2^2 x 3^2 x 5^2 = 180
Therefore, there are a total of 1+4+9+1+36+20+45+180 = 296 factors of 10800 that are perfect squares.
Hence, the correct option is (B) 12.
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How many factors of 10800 are perfect squares?a)6 b)12 c)8 d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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