Find the number of positive integers between 1 and 2300 inclusive that are relatively prime to 700.
I have no idea how to approach this question, honestly.
[Math] Number of positive integers between 1 and 2300 inclusive that are relatively prime to 700.
combinatorics
Related Solutions
HINT:
Let integer $d$ divides both $a+bk, b$
$\implies d$ divides $a+bk-k(b)=a$
$\implies d$ divides $a,b$
There is one number with all three digits equal to 5.
There are 1x10x10 = 100 numbers with the first digit equal to 5.
There are 9x1x10 = 90 numbers with the second digit equal to 5.
There are 9x10x1 = 90 numbers with the third digit equal to 5.
There are 10 numbers with the first and second digit equal to 5.
There are 10 numbers with the first and third digit equal to 5.
There are 9 numbers with the second and third digit equal to 5.
There are 8x9x9 = 648 numbers with no digit equal to 5.
This is enough information to fill in the diagram above.
Best Answer
Hints: 1) $700$ is divisible by $2$, $5$ and $7$.
2) Inclusion-Exclusion principle.