Question

6. What is the number of ways in which 11025 can be
expressed as the product of a pair of co-primes?​

Answer 1

Answer:

4

Step-by-step explanation:

More generally, suppose n>1 and let n=∏i=1rpeii, where the pi’s are primes. In order for d∣n to be coprime to nd, we must have d=∏i∈I⊆{1,2,3,…,r}peii. Thus there are as many ordered pairs (d,nd) as there are subsets of {1,2,3,…,r}. Since we are interested in counting unordered pairs {d,nd}, we have 122r=2r−1

expressions as product of pairs of coprimes.

Note that there is only one way to express 1

as a product of a pair of coprimes.

For n=32⋅52⋅72

has 3 distinct prime factors, the number of expressions a product of coprimes is 22=4. These are {1,32⋅52⋅72}, {32,52⋅72}, {52,32⋅72}, {72,32⋅52}.

Answer 2

Answer:

u can simply factorise it...... and can express it in that coprime no.