Answer:
No, It is not necessarily true that the greatest common divisor of all three numbers is greater than 1.
Step-by-step explanation:
Consider the provided information.
It is given that Aisha's number and Benoit's number have a common divisor greater than 1.
Let us assume any number having common divisor greater than 1
Let say Aisha's number is 10 and Benoit's number is 14.
Now the common divisor in both the numbers are:
Aisha: 10 = 2×5
Benoit: 14 = 2×7
Here, the common divisor is 2.
Now, it is given that Aisha's number and Carleen's number also have a common divisor greater than 1.
Let us assume Carleen's number is 35. Thus the common divisor in both the numbers are:
Aisha: 10 = 2×5
Carleen: 35 = 5×7
Here, the common divisor is 5.
Benoit's number and Carleen's number also have a common divisor greater than 1.
Benoit: 14 = 2×7
Carleen: 35 = 5×7
Here, the common divisor is 7.
Now, we need to find that the greatest common divisor of all three numbers is greater than 1.
Aisha: 10 = 2×5
Benoit: 14 = 2×7
Carleen: 35 = 5×7
There is no common divisor greater than 1.
Hence, it is not necessarily true that the greatest common divisor of all three numbers is greater than 1.
