The given equation is ax + by = 5.

The greatest common divisor (gcd) of two numbers is the largest number that divides both of them without leaving a remainder.

In this case, we are asked to find the gcd of x and y.

From the given equation, we can see that both x and y are factors of 5.

However, it is also given that 55 does not divide x. This means that x cannot be a multiple of 55.

Since 5 is a prime number, the only possible values for x and y that satisfy the equation are multiples of 5 that are not multiples of 55.

Therefore, the gcd of x and y in this case is 5.

Question

The given equation is ax + by = 5.

The greatest common divisor (gcd) of two numbers is the largest number that divides both of them without leaving a remainder.

In this case, we are asked to find the gcd of x and y.

From the given equation, we can see that both x and y are factors of 5.

However, it is also given that 55 does not divide x. This means that x cannot be a multiple of 55.

Since 5 is a prime number, the only possible values for x and y that satisfy the equation are multiples of 5 that are not multiples of 55.

Therefore, the gcd of x and y in this case is 5.

Knowee AI · Accepted Answer

The given equation is ax + by = 5.

The greatest common divisor (gcd) of two numbers is the largest number that divides both of them without leaving a remainder.

In this case, we are asked to find the gcd of x and y.

From the given equation, we can see that both x and y are factors of 5.

However, it is also given that 55 does not divide x. This means that x cannot be a multiple of 55.

Since 5 is a prime number, the only possible values for x and y that satisfy the equation are multiples of 5 that are not multiples of 55.

Therefore, the gcd of x and y in this case is 5.

Suppose there are integers 𝑎𝑎, 𝑏𝑏, 𝑥𝑥 and 𝑦𝑦 such that 𝑎𝑥+𝑏𝑦=5𝑎𝑥+𝑏𝑦=5, and 55 does not divide 𝑥𝑥. What is gcd(𝑥,𝑦)gcd(𝑥,𝑦)?