How many factors of 878800000 are perfect squares?

M4maths Previous Puzzles

19 Jul 2017 Perfect Squares

How many factors of 878800000 are perfect squares?

OPtion

1) 8
2) 27
3) 18
4) 12
5) 24
6) 16
7) 36
8) 32
9) 48
10) None of these

Solution

878800000 = 2^7* 5^5 * 13^3

Any factor of this number should be of the form 2^a * 5^b * 13^c.

For the factor to be a perfect square a,b,c have to be even.

a can take values 0, 2, 4, 6
b can take values 0, 2, 4
and c can take values 0, 2

Total number of perfect squares = 4 * 3 * 2 = 24

Correct Option: 5 Best Solution (4)

yamini velaga   7 years AGO

878800000 = (2^7) × (5^5) × (13^3)
Any factor of 878800000 can be expressed as (2^a) × ( 5^b) × (13^c)
a,b,c should be even numbers
possibilities for a,b,c are
a -------> 0,2,4,6 ----- 4 possibilities
b--------> 0,2,4 --------3 possibilities
c--------> 0,2 -----------2 possibilities
no.of perfect squares among the factors of 878800000 = 4×3×2 = 24

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G.S.Kantharao   7 years AGO

Given = 878800000
Product of prime factors = (2^7)*(5^5)*(13^3)
Factors which are also perfect squares from the above are= 1,4,16,25,64,100,169,400,625,676,1600,2500,2704,4225,10000,10816,16900,40000,67600,270400,422500,1081600,1690000,6760000 (Total no.24)
Hence the right option is 5👈

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Mukund Manohar   7 years AGO

Factors of 878800000 = 2^7 * 5^5 * 13^3
Values for perfect square = 2^0,2^2,2^4,2^6 = 4 values
Values for perfect square = 5^0,5^2,5^4 = 3 values
Values for perfect square = 13^0,13^2 = 2 values
Total Values = 4*3*2 = 24
24 factors of 878800000 are perfect squares.

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jksdvs   7 years AGO

1000000*13*13 and 26 remains 169 and 100 100 100 forms perfect so there are 4 numbers which forms perfect squares they can be shuffled in 24 ways

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