Shell Script to find biggest of three numbers using nested if

Program

#! /bin/bash
echo "Enter value of 'a':"
read a
echo "Enter value of 'b':"
read b
echo "Enter value of 'c':"
read c
if [ $a -gt $b ]
then
    if [ $a -gt $c ]
    then 
     echo "a is greatest"
    else
     echo "c is greatest"
    fi
else
    if [ $b -gt $c ]
    then 
    echo "b is greatest"
    else
    echo "c is greatest"
    fi
fi

Output 1

$ ./biggest-of-three-nested-if.sh 
Enter value of 'a':
6
Enter value of 'b':
3
Enter value of 'c':
2
a is greatest

Output 2

$ ./biggest-of-three-nested-if.sh 
Enter value of 'a':
5
Enter value of 'b':
6
Enter value of 'c':
3
b is greatest

Output 3

$ ./biggest-of-three-nested-if.sh 
Enter value of 'a':
3
Enter value of 'b':
5
Enter value of 'c':
9
c is greatest