The product of all digits of a 4 digit number is 630. How many such numbers can be made. all the dig

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10 Dec 2014 4 digit number problem

The product of all digits of a 4 digit number is 630. How many such numbers can be made. all the digits of the given number are different

OPtion

1). 12
2). 20
3). 24
4). 26
5). 36
6). 48
7). 64
8). 100
9). 112
10). 120

Solution

Product = 630
= 2*3*3*5*7
Only 2 prossibility is there
2 x 9 x 5 x 7
Or
3 x 6 x 5 x 7

2, 9, 5, 7 can be arranged in 4 x 3 x 2 x 1 = 24 ways similarly other
So answer will be 48.

Correct Option: 6 Best Solution (20)

RAKESH   10 years AGO

630 = 2*5*7*9 = 3*5*6*7

4! + 4! = 48

Like? Yes (9) | No (3)  

Rajat Rokade   10 years AGO

630=2*3*3*5*7
Now,
four digit number are to be formed out of these numbers.
only two numbers 7529 and 7563 are possible.
So, possible combinations = 4! + 4!
=48. So option 6) is correct.

Like? Yes (3) | No (1)  

HARMEET KAUR   10 years AGO

Possible set of digits are 2,5,7,9 & 3,5,6,7 .
so possible numbers = 2 x (4*3*2*1) =48

Like? Yes (3) | No (1)  

Pramod Gaikwad   10 years AGO

only two numbers 7529 and 7563 are possible.
So, possible combinations = 4! + 4!
=48.
So option 6)

Like? Yes (2) | No (1)  

SAYAN CHATTERJEE   10 years AGO

the factors of 630 are 2,5,3,3,7
they can be togetherly taken in four digits as the permutations of (9527) and (6537). so the no. of such numbers will de (4!+4!= 48) (6)

Like? Yes (1) | No   

P.Nikhil Reddy   10 years AGO

Take LCM 0f 630....you get factors as ,7,3,3,2,5....now no number can be clubbed with 7 & 5..as they become 2 digits..

hence digits can be 7,5,2,9(3*3), or 7,5,3,6(2*3).....therefore these 4 digits can be arranged in 4! ways ...

hence 7,5,2,9 (24) ..7,5,3,6(24)...

total 48

Like? Yes (2) | No (1)  

K.ARun   10 years AGO

2,5,7,9 and 6,5,7,3 are the only 4digit no. which leads to the product of 630.
2,5,7,9 by permutation we will get 24combinations and 6,5,7,3 by permutation we will get 24combinations These are the possible combinations for 4digit nos.
with these we can make 48possible combinations

Like? Yes (4) | No (3)  

kumari jyoti   10 years AGO

there are two sets of digits possible. 7,5,3,6 and 7,5,9,2.
now for the arrangement of 4 digits for a number without repetition is 4! i.e. 24 and there are two sets of numbers. so, the answer is 48.

Like? Yes (2) | No (1)  

Sravanthi   10 years AGO

6 5 3 7 (24 combinations)
9 2 5 7
total 2 sets of 24=48

Like? Yes (2) | No (1)  

murari kumar   10 years AGO

630=2*3*3*5*7
630=2*9*5*7 and 3*6*5*7
using above digits four digit no can be formed = 24+24=48

Like? Yes (2) | No (1)  

sanjeev kumar   10 years AGO

Ans 48

Like? Yes (1) | No   

BHASKAR MANDAL   10 years AGO

possibilities 2,5,7,9 and 3,6,5,7
so 2*4! =48
option 6

Like? Yes (1) | No   

Revathi   10 years AGO

factors of 630 = 2*3*3*5*7
since it is a 4 digit number the factors can be arranged as 2*5*7*9 and 3*5*6*7
2579 = 24 combinations
3567 = 24 combinations
total 48.

Like? Yes (1) | No   

Mithun Kumar Kesari   10 years AGO

630=8*7*2*5

case1: digits= 2,5,7,9
possible numbers= 4!= 24
case 2: digits= 3,5,6,7
possible numbers= 4!= 24


so total no. =48

Like? Yes (1) | No   

Rajeev Kumar Garikapati   10 years AGO

7,3,3,5,2 are the factors of 630...
So, the four digits are 7952 and 7365
both have 4! + 4! = 48.

Like? Yes (1) | No   

Chandra chur anand   10 years AGO

factor of 630=2*5*3*3*7
so 4 digit no. ll be 2597 so arrangment from these 4 no. ll be 24
and another no. is 6537 so again arrangement ll be 24
hence total n. ll be 48 ans.... confirmed!!!

Like? Yes (1) | No   

Anjali   10 years AGO

two combinations possible:
(2,9,5,7) - 4! ways
(6,3,5,7) - 4! ways
total = 48 ways

Like? Yes (1) | No   

Vinay Sipani    10 years AGO

630 = 2 * 3 * 3 * 5 * 7

As all the digits are different,possible combinations are
6*5*3*7 , 2*9*5*7

Digits of 6537 can be arranged in 4! = 241 ways
Digits of 2957 can be arranged in 4! = 24 ways

=> 48 numbers are possible.

Like? Yes (1) | No (1)  

Dr.Dipin Singh   10 years AGO

Possible set of digits are 3,5,6,7 and 2,5,7,9.
so number of such numbers = 2*(4*3*2*1)=48

Like? Yes (2) | No (2)  

Manasa Kotha   10 years AGO

7635=4*3*2*1=24
7295=4*3*2*1=24
so total 48

Like? Yes (1) | No (1)