Latest TCS Aptitude Question SOLUTION: what is the total no of factors of 16!?

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(#M40038066) TCS Numerical Ability question number system Keep an EYE

what is the total no of factors of 16!?

Asked In TCS Gourab Dutta (9 years ago)

Unsolved Read Solution (9)

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Read Solution (9) :

Niraj Ojha  (9 years ago)

16!=1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16
=2*3*2*2*5*2*3*7*2*2*2*3*3*2*5*11*2*2*3*13*2*7*3*5*2^4
2^15*3^6*5^3*7^2*11*13
So no. Of factor =16*7*4*3*2*2
=448*12
= 53 76

Is this solution Helpfull? Yes (30) | No (2)  

Udai Pratap Singh  (9 years ago)

==>1* 2* 3* 4* 5 *6 *7 *8 *9 *10 *11* 12* 13 *14* 15 *16

==>(2^15)*(3^6)*(5^3)*(7^2)*(11^1)*(13^1)
total no of factors=>(15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1)
=>16*7*4*3*2*2
[ans==>5376]

Is this solution Helpfull? Yes (12) | No   

jayakarthi K R  (9 years ago)

this question can be solved based on splitting the numbers into basic co-primes. to split a number as possible into the co primes.
for 16!
2*3*......15*16
to split number based on coprimes
(2^15)*(3^6)*(5^3)*(7^2)*(11^1)*(13^1)
ie: (x^n)*(y^n) so the no of factors are (n+1)*(n+1)
16*7*4*3*2*2
=5376

Is this solution Helpfull? Yes (6) | No   

akshay  (9 years ago)

5376
1* 2* 3* 4* 5 *6 *7 *8 *9 *10 *11* 12* 13 *14* 15 *16

(2^15)*(3^6)*(5^3)*(7^2)*(11^1)*(13^1)
total no of factors=(15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1)
16*7*4*3*2*2
[ans 5376

Is this solution Helpfull? Yes (2) | No   

Pranay Banerjee  (9 years ago)

16!=1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16
=2*3*2*2*5*2*3*7*2*2*2*3*3*2*5*11*2*2*3*13*2*7*3*5*2^4
2^15*3^6*5^3*7^2*11*13
So no. Of factor =16*7*4*3*2*2
=448*12
= 5376

Is this solution Helpfull? Yes (2) | No   

BISWAJIT NATH  (9 years ago)

guys why have u multiplied the number of factors. it is asked to find the total number of factors n 16!. shouldn't we add the number of factors to get the total number of factors????

Is this solution Helpfull? Yes (1) | No (7)  

Saurav Sunny  (9 years ago)

16!= 2^15 * 3^6 * 5^3 * 7^1 * 13^1 where 2,3,5,7,13 are the prime no. less then 16 then total number of factors is equal to 16*7*4*2*2

Is this solution Helpfull? Yes | No (2)  

Dharmendra Shukla  (9 years ago)

2^15*3^6*5^3*7^2*11^1*13^1 i.e
a^p*b^q.................z^r
then
total factors=(p+1)*(q+1)...............
so
16*7*4*3*2*2=5376

Is this solution Helpfull? Yes | No (1)  

shilpi saini  (9 years ago)

17 factors are there in 16! i.e 1,2......16 and 16! itself

Is this solution Helpfull? Yes | No (8)  

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