A philosopher of science is contemplating the symmetry of natural laws and wonders: If the sum of two positive integers $a$ and $b$ equals 2023, what is the largest possible value of $\gcd(a, b)$?

February 22, 2026

$A philosopher of science is contemplating the symmetry of natural laws and wonders: If the sum of two positive integers $a$ and $b$ equals 2023, what is the largest possible value of $\gcd(a, b)$?$

Area of one equilateral triangle: $\frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3}$.
Total area = $6 \times 9\sqrt{3} = 54\sqrt{3}$ cm².
#### $54\sqrt{3}$ cm²**Question:
To maximize $\gcd(a, b)$, we note that if $\gcd(a, b) = d$, then $a = dx$ and $b = dy$ for some integers $x$ and $y$ with $\gcd(x, y) = 1$. Thus, $a + b = dx + dy = d(x + y) = 2023$. Therefore, $d$ must divide 2023.
First, we factor 2023 to find its divisors. Checking small prime numbers:
2023 is odd, so not divisible by 2.

A philosopher of science is contemplating the symmetry of natural laws and wonders: If the sum of two positive integers \(a\) and \(b\) equals 2023, what is the largest possible value of \(\gcd(a, b)\)?

Related Articles

Trending Articles