MHB Calculating Numbers with Common Factors: A Scientific Approach

[evinda]

Hello! (Wave)

I am looking at the following exercise:

Find how many numbers $k$ with $1 \leq k \leq 3600$ exist,that have at least one common factor $>1$ with $3600$.

I thought that the number we are looking for is equal to:
$$3600-\phi(3600)=3600-\phi(2^4 \cdot 3^2 \cdot 5^2 )=3600-3600(1-\frac{1}{2})(1-\frac{1}{3})(1-\frac{1}{5})=3600 \cdot \frac{11}{15}=2640$$

Could you tell me if it is right? (Thinking) (Nerd)

 

[M R]

Hello! (Wave)

I am looking at the following exercise:

Find how many numbers $k$ with $1 \leq k \leq 3600$ exist,that have at least one common factor $>1$ with $3600$.

I thought that the number we are looking for is equal to:
$$3600-\phi(3600)=3600-\phi(2^4 \cdot 3^2 \cdot 5^2 )=3600-3600(1-\frac{1}{2})(1-\frac{1}{3})(1-\frac{1}{5})=3600 \cdot \frac{11}{15}=2640$$

Could you tell me if it is right? (Thinking) (Nerd)

That's right. :)

 

[evinda]

That's right. :)

Great! Thanks a lot! (Happy)