Məxrəci 115 olan ixtisar olunan düzgün kəsrlər
Published:
25. Məxrəci 115 olan neçə ixtisar olunan düzgün kəsr var? A) 10 B) 28 C) 21 D) 8 E) 26
Animated Video Solution
The first half plays free, the full solution is in the app.
Step by Step Written Solution
Let's solve the problem: How many proper fractions with a denominator of 115 can be simplified?
Understanding the Problem
A proper fraction with denominator 115 is written as $\frac{n}{115}$, where $1 \le n < 115$.
A fraction can be simplified if the numerator and the denominator share a common factor greater than one. First, let's find the prime factorization of 115.
Since 115 is five times 23, a fraction $\frac{n}{115}$ can be simplified if the numerator n is a multiple of 5 or a multiple of 23.
We need to count $n$ such that $1 \le n < 115$ and $\gcd(n, 115) > 1$.
First, let's count the multiples of 5 that are less than 115. We divide 115 by 5, which is 23, and subtract one because we need proper fractions, so we count up to 110. That gives us 22 multiples.
The rest of this solution is on Solvi
4 more steps are locked. Watch the full animated, narrated solution for free.
Snap a photo, solve any question like this.
Watch the Rest for Free
Free to download · First solutions are on us
