Forming Greatest and Smallest 6-Digit number using Given Digits.

FORMING GREATEST AND SMALLEST NUMBER WITH THE GIVEN DIGITS:

In some cases,the given digits from which the number to be formed are lesser than the digits in the number formed.In such case, we need to use Repetition of digits in formation of greatest and smallest number.

Form  Greatest and Smallest 6^th digit number.

1) Digits: 3,7,8,4,9  

Answer:

a) Greatest Number:

Here, the number of digits given are lesser than the digit to be formed.

So, to form greatest number with the given digits ,the greater digit is repeated.

In the given digits, the greater number is ‘9’, which is to be repeated.

Step-1: The number of digits given = 5.

The number to be formed is 6^th digit number, which need one more digit.

 Step-2: Descending Order of the given digits:  9 > 8 > 7 > 4 > 3 .    

Step – 3: The digit 9, which is greater need to put in two place values. i.e; Lakhs(L) , TenThousands(TTh) ,  the next greater numbers are placed in next  place values.

Lakhs    (L)	TenThousands       (TTh)	Thousands     (Th)	Hundreds     (H)	Tens   (T)	Ones   (O)
9	9	8	7	4	3

 

Thus the greatest number formed is :  9,98,743.

 

b) Smallest number:

The given digits are: 3,7,8,4,9  

To form smallest number with the given digits ,the smaller digit is repeated.

In the given digits, the smaller number is ‘3’, which is to be repeated.

Step-1: The number of digits given = 5.

The number to be formed is 6^th digit number, which need one more digit.

Step-2 : The Ascending order of the given digits : 3 < 4 < 7 < 8 < 9 .  

Step – 3: The digit 3, which is smaller need to put in two place values. i.e; Lakhs(L) , TenThousands(TTh) ,  the next smaller numbers are placed in next  place values.

Lakhs    (L)	TenThousands       (TTh)	Thousands     (Th)	Hundreds     (H)	Tens   (T)	Ones   (O)
3	3	4	7	8	9

 

 

2) Digits :  3 , 1 , 8 , 0  

a) Greatest Number:

Here, the number of digits given are lesser than the digit to be formed.

So, to form greatest number with the given digits ,the greater digit is repeated.

In the given digits, the greater number is ‘ 8’, which is to be repeated.

Step-1: The number of digits given = 4.

The number to be formed is 6^th digit number, which need two more digits.

Step-2:  Descending Order of the given digits:  8 > 3 > 1 >0 .

Step – 3: The digit  8, which is greater need to put in two place values. i.e; Lakhs(L) , TenThousands(TTh) ,  the next greater numbers are placed in next  place values.

Lakhs    (L)	TenThousands       (TTh)	Thousands     (Th)	Hundreds     (H)	Tens   (T)	Ones   (O)
8	8	8	3	1	0

 

Thus the greatest number formed is :  8,88,310 .

 

b) Smallest number:

The given digits are: 3 , 1 , 8 , 0 . 

To form smallest number with the given digits ,the smaller digit is repeated. Here, digit ‘ 0 ‘ is in the given digits. So, we need to check the next smaller number which is smaller in the given digits i.e; ‘1’.

First, digit ‘1’  has to put in greatest place value,then the digit ‘0’ is repeated three times in the next corresponding place values followed by next three digits in the next place values to form smallest 6^th digit number.

In the given digits, the smaller number is ‘0’, which is to be repeated.

Step-1: The number of digits given = 4.

The number to be formed is 6^th digit number, which need two more digits.

Step-2 : The  Ascending order of the given digits : 0 < 1 < 3  < 8 .  

Step – 3: The digit ‘1’, which is smaller need to put greatest place value . i.e; Lakhs(L) , digit ‘0’ is placed in TenThousands(TTh) ,Thousands(Th) ,Hundreds(H) , the next smaller numbers are placed in next  place values.

Lakhs    (L)	TenThousands       (TTh)	Thousands     (Th)	Hundreds     (H)	Tens   (T)	Ones   (O)
1	0	0	0	3	8

Thus, the smallest number formed is : 1,00,038.

 

The Table shows building the Greatest and Smallest 6^th digit number with the given digits:

S.NO	DIGITS	GREATEST NUMBER	SMALLEST NUMBER
1	3, 1, 4	4,44,431	1,11,134
2	8,0,3,6,4	8,86,430	3,00,468
3	9,2, 6,7	9,99,762	2,22,679