Subjects number theory

Common Divisors Cdbdb7

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Common Divisors Cdbdb7


1. The problem is to find numbers by which you can divide two or three given numbers. 2. To solve this, we use the concept of the Greatest Common Divisor (GCD), which is the largest number that divides two or more numbers without leaving a remainder. 3. The formula for GCD of two numbers $a$ and $b$ is often found using the Euclidean algorithm. 4. For three numbers $a$, $b$, and $c$, the GCD is $\gcd(a,b,c) = \gcd(\gcd(a,b), c)$. 5. Important rule: The GCD divides each of the numbers exactly. 6. Example: If the numbers are 12, 18, and 24, then $\gcd(12,18) = 6$ and $\gcd(6,24) = 6$, so 6 divides all three numbers. 7. Therefore, the numbers you can divide with are all divisors of the GCD. 8. To find all such numbers, find all divisors of the GCD. 9. This method works for any two or three numbers to find common divisors.