Latest MBA Aptitude Question SOLUTION: in how many ways can 2310 be expressed as product of three factors??

1) 41
2) 56
3) 23
4) 46

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in how many ways can 2310 be expressed as product of three factors??

1) 41
2) 56
3) 23
4) 46

Asked In MBA (11 years ago)

Unsolved Read Solution (7)

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RIDDHI RANJAN DE  (9 years ago)

(3^(n-1)+1)/2
2310=2*3*5*7*11
n=5
do this

ans===41

Is this solution Helpfull? Yes (31) | No (8)  

Tania Chatterjee  (9 years ago)

2310 = 2*3*5*7*11....
A product of 1st 5 prime numbers... 5 Factors!


U need to take the product of 3 factors out of these 5 factors....
Which can be taken in two ways.....
{1 Factor}*{1 Factor}*{the rest 3 Factors}
or {1 Factor}*{2 Factors}*{the rest 2 Factors}

1st Case: There are 5*4 ways = 20 Ways
2nd Case: There are 5*6(4C2) ways = 30 Ways

A total of 50 ways in which 2310 can be expressed as a product of three factors....

Is this solution Helpfull? Yes (6) | No (15)  

kislay kumar  (8 years ago)

The Prime factors of 2310 are 2, 3, 5, 7 and 11, as 2310 = 2*3*5*7*11.
Now, when 2310 is a product of three factors, two cases arise. (a) when 1 is one of the factors or the other case of two of the factors are 1's and (b) 1 is not one of the three factors.
Lets consider each of the cases individually with examples.

When two of the factors are 1's So, it should be 1 * 1* 2310. It can happen in only one way.
When 1 is one of the factors, for example 1*11*210 , here as one of the factors is 1, the remaining 5 prime factors are to be divided into two groups. So, five numbers into two groups, it can be 4 and 1 or 3 and 2
So, 1 * 4 factors * 1 factor - It can happen in 5 ways
Or, 1 * 3 factors * 2 factors, this can happen in 5c3 = 10 ways

Now the second case of 1 is not one of the factors,
5 factors are to be divided into three groups, this can be

3 factors * 1 factor * 1 factor- this can happen in 5c3 ways=10
2 factors * 2 factors & 1 factor- this can happen in 5c2 * 3c2 = 30 ways

Total = 1+5+10+10+30 = 56 ways

Is this solution Helpfull? Yes (3) | No (6)  

sahil gupta  (10 years ago)

2310 = 2*3*5*7*11
When a number can be expressed as a product of n distinct primes,
then it can be expressed as a product of 3 numbers in (3^(n+1) + 1)/2 ways

Is this solution Helpfull? Yes (1) | No (6)  

ganesh babu  (8 years ago)

Ans:56
1*1*2310
1*2*(3*5*7*11)
1*3*(2*5*7*11)
1*5*(2*3*7*11)
1*7*(2*3*5*11)
1*11*(2*3*5*7)
...
...

Is this solution Helpfull? Yes (1) | No (8)  

NIVE  (5 years ago)

1 is the ans

Is this solution Helpfull? Yes | No (1)  

vijay subramanian A T  (4 years ago)

1 is the answer

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