Question

In how many ways 30142 can be written as a product of 2 numbers

Answer 1

I am not sure .. but I think 7 ways....

Answer 2

Answer:

The number of ways such that 30142 can be represented as a product of two numbers is:

                          4

Step-by-step explanation:

We know that any number 'n' of the form:

$n=(a_1)^{p_1}(a_2)^{p_2}(a_3)^{p_3}.........(a_k)^{p_k}$

Then the number of divisors of n is given by:

$Number\ of\ divisors=(p_1+1)(p_2+1)......(p_k+1)$

Hence, if number of divisors is even then the number of ways it can be written as a product of two numbers is:

Number of divisors/2

If number of divisors is odd then the number of ways it can be written as a product of two numbers is:

(Number of divisors+1)/2

( Such a thing happens due to symmetry as a×b=b×a is the same representation )

Hence here we have the number as:

n=30142

$n=(2)^1(7)^1(2153)^1$

Hence, number of divisors of n is:

$Number\ of\ divisors=(1+1)(1+1)(1+1)\\\\Number\ of\ divisors=2\times 2\times 2\\\\Number\ of\ divisors=8$

Hence, the number of ways of writing 30142 as a product of 2 numbers is:

                                     4

(Since 8/2=4)