Question

There are 260 cadets and 312 junior officers at an army training camp. All of the cadets and junior officers at the training camp are divided into identical teams, so that all of the teams have the same number of cadets and the same number of junior officers. What is the largest number of teams that there could be?​

Answer 1

To find the largest number of teams that there could be, we need to determine the greatest common divisor (GCD) of the number of cadets and junior officers.

The GCD represents the largest number that divides both the number of cadets and the number of junior officers evenly, without leaving any remainder. This will give us the maximum number of teams that can be formed, with each team having an equal number of cadets and junior officers.

Given that there are 260 cadets and 312 junior officers, we can calculate the GCD using various methods such as prime factorization, Euclidean algorithm, or a calculator.

Using the prime factorization method:

The prime factorization of 260 is 2^2 * 5 * 13.

The prime factorization of 312 is 2^3 * 3 * 13.

To find the GCD, we take the product of the common prime factors with the lowest exponents:

GCD = 2^2 * 13 = 52

Therefore, the largest number of teams that there could be is 52. Each team would have an equal number of cadets and junior officers.

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