Let's solve this problem step by step.
### (i) The possible numbers of friends to whom the snickers can be equally distributed
We need to find all the factors of 24. Factors of a number are the numbers that divide it completely without any remainder.
Factors of 24:
1, 2, 3, 4, 6, 8, 12, 24
So, the possible numbers of friends to whom the snickers can be equally distributed are:
[tex]\[ 1, 2, 3, 4, 6, 8, 12, 24 \][/tex]
### (ii) The possible numbers of friends to whom the cadburies can be equally distributed
Similarly, we need to find all the factors of 36.
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
So, the possible numbers of friends to whom the cadburies can be equally distributed are:
[tex]\[ 1, 2, 3, 4, 6, 9, 12, 18, 36 \][/tex]
### (iii) The possible numbers of friends to whom both the snickers and cadburies can be equally distributed
To find the common numbers of friends for distributing both snickers and cadburies, we need to find the common factors of 24 and 36.
Common factors of 24 and 36:
[tex]\[ 1, 2, 3, 4, 6, 12 \][/tex]
So, the possible numbers of friends to whom both the snickers and cadburies can be equally distributed are:
[tex]\[ 1, 2, 3, 4, 6, 12 \][/tex]
### (iv) The greatest number of friends to whom both the snickers and cadburies can be equally distributed
The greatest number in the list of common factors is the greatest common divisor (GCD) of 24 and 36.
GCD of 24 and 36:
[tex]\[ 12 \][/tex]
So, the greatest number of friends to whom both the snickers and cadburies can be equally distributed is:
[tex]\[ 12 \][/tex]
### (v) How many snickers and cadburies does each friend get when distributed equally among the greatest number of friends
We have determined that the greatest number of friends is 12.
The number of snickers each friend gets:
[tex]\[ \text{snickers per friend} = \frac{24}{12} = 2 \][/tex]
The number of cadburies each friend gets:
[tex]\[ \text{cadburies per friend} = \frac{36}{12} = 3 \][/tex]
So, each friend gets:
[tex]\[ 2 \text{ snickers} \][/tex]
[tex]\[ 3 \text{ cadburies} \][/tex]
### Summary
1. Possible numbers of friends for snickers: [tex]\[ 1, 2, 3, 4, 6, 8, 12, 24 \][/tex]
2. Possible numbers of friends for cadburies: [tex]\[ 1, 2, 3, 4, 6, 9, 12, 18, 36 \][/tex]
3. Possible numbers of friends for both: [tex]\[ 1, 2, 3, 4, 6, 12 \][/tex]
4. Greatest number of friends for both: [tex]\[ 12 \][/tex]
5. Each friend gets: [tex]\[ 2 \text{ snickers and } 3 \text{ cadburies} \][/tex]
