# Aptitude - Numbers - Discussion

### Discussion :: Numbers - General Questions (Q.No.65)

65.

If the number 42573 * is exactly divisible by 72, then the minimum value of * is:

 [A]. 4 [B]. 5 [C]. 6 [D]. 7 [E]. 8

Explanation:

72 = 9 x8, where 9 and 8 are co-prime.

The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.

Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.

Required value of * is 6.

 Soniya said: (Jul 1, 2011) Sir, I am unable to solve this, because when x=6 then we get 27 which is divided by 9 not by 8, then how answer is x=6.

 Faizal said: (Feb 24, 2012) The divisibility rule for 8 is : You have to take the last 3 digit no and divide it by 8 if it is divisible by then the no will be divisible by 8. Hope you understood.

 Rajasekar said: (Nov 7, 2014) There is a simple way:- 72 is a multiple of 3, since 42573x is divisible by 72 (given). Hence: 4+2+5+7+3+x = 21+x (which must be a divisible by 3). From the given options 6 is the only option which fits in place of x to satisfy the above criteria. Hope you understood.

 Ashith said: (Jan 9, 2015) 72 = 2^3+3^2. Apply divisibility rule of 2 and 3 on 42573x. 4+2+5+7+3+x = 21+x should be divisible by 3 if and only if x is 6.

 Rampavan said: (Mar 8, 2015) Good problem and Easy for solving is also available.

 Ritvik said: (Aug 12, 2015) If you count the digits except * it comes to be 21. Now place one by one options and add it up and check the divisibility by 3. Only option C and D satisfies but option D doesn't satisfy divisibility rule of 9. Clearly answer is 6 i.e. option C.

 Koti Ch said: (Mar 4, 2016) May I know about co prime numbers?

 Saravanan said: (Mar 4, 2016) Easy method: 72 is always divisible by(9*8), Note: always take the minimum value here min value is : 8. Now take the last 3 digits and place 8 in place of 'x'. Then use all the given options, Ex: 73* => 738/4 it will not give. So by the way we can get only by using 6. i.e: 738/6 = 123. Hence the answer: 6. Thank you.

 Atul said: (Jul 21, 2016) 72 is known that is divisible by 3. And any number, multiplied by 72 will be even. And, 4 + 2 + 5 + 7 + 3 = 21, which is divisible by 3 "known". We need to find an option from rest of the options which is even and divided by 3.

 Shree said: (Jul 5, 2017) 425736/72 =6.

 Pankaj Verma 9041939259 said: (Nov 15, 2017) 73x is divisible by 8 is, x = ? First divide 73/8. 8x9 = 72 remainder 1. 73 1 X we need 6(1 is remainder while dividing 73 with 8 after remainder we have to put the value of X). 1X/8 as we know 16/8 so X is 6.

 Vinod said: (Feb 7, 2019) Why should a take 6 and 73x?

 Arun Prasanth V said: (Feb 9, 2019) 42573* รท 72, First we do, 72 = 9*8. Then, The sum of num 42573* is divisible are not divisible by 9, 4+2+5+7+3+x = 21+x, Now see we take 6 to add and then the number is divisible, 21+6= 27 now it is divided so the x =6.

 Nandini said: (Sep 28, 2019) How 6 will be the answer? please explain.