A group of 290 men from National Cadet Cops and 612 men from National Police Cadet Corps were selected to peform at the National Day parade. On the day of the performance, 12 fell sick, 6 of them from the National Cadet Corps and the remaining from the National Police Cadet Corps. They were then divided into as many groups as possible with the same number of men from both the National Cadet Corps and National Police Cadet Corps. Find
(a)the largest number of groups that could be formed.
(b)the number of National Cadet Corps men in a group
To find the largest number of groups that could be formed, we need to find the greatest common divisor (GCD) of 290 and 612. This can be done using the Euclidean algorithm:
Step One: Divide 612 by 290. The remainder is 32.
Step Two: Divide 290 by 32. The remainder is 18.
Step Three: Divide 32 by 18. The remainder is 14.
Step Four: Divide 18 by 14. The remainder is 4.
Step Five: Divide 14 by 4. The remainder is 2.
Step Six: Divide 4 by 2. The remainder is 0.
The last non-zero remainder is 2, so the GCD of 290 and 612 is 2.
(a) The largest number of groups that could be formed is equal to the GCD, which is 2.
(b) The number of National Cadet Corps men in a group can be found by dividing 290 by the GCD: 290/2 = 145.
Therefore, the number of National Cadet Corps men in a group is 145.