The greatest common factor of 63 and a positive integer a is 9, and the greatest common factor of a and 30 is 3. Which of the following could be the greatest common factor of a and 270?
Answers
Topic
Greatest Common Factor
Given
The greatest common factor of 63 and a positive integer 'a' is 9, and the greatest common factor of 'a' and 30 is 3.
To Find
The greatest common factor of 'a' and 270.
Method
Calculate value of 'a' and then find greatest common factor of 'a' and 270.
Solving
The greatest common factor of 'a' and 63 is 9.
It means number 'a' is divisible by 9 and it is from 9 to 54.
So, possible values of 'a' are 9, 18, 27, 36, 45 and 54.
Now,
The greatest common factor of 'a' and 30 is 3.
It means number 'a' is divisible by 3 and it is from 3 to 30.
All numbers divisible by 9 are divisible by 3.
So,
'a' is from 9, 18, 27 only as it is from 9 to 30.
We will check for above values
Check for a = 9
GCF of 9 and 63 is 9.
GCF of 9 and 30 is 3.
So, 9 satisfies the requirements for 'a'.
Check for a = 18
GCF of 18 and 63 is 9.
GCF of 18 and 30 is 6.
So, 18 don't satisfies requirements for 'a'.
Check for a = 27
GCF of 27 and 63 is 9.
GCF of 27 and 30 is 3.
So, 27 satisfies requirements for 'a'
So, a can be 9 and 27.
Now,
GCF of 9 and 270 will be 9.
GCF of 27 and 270 will be 27.
Answer
If
a = 9 then GCF of 9 and 270 is 9.
a = 27 then GCF of 27 and 270 is 27.