Question

make two 4-digit numbers using each of the digits 1, 2, 4, and 5 such that the numbers made are divisible by 132



STAPE -Y -STAPE EXPENITION​

Answer 1

Answer:

Given:  4-digits numbers using each the digits 1,2,4 and 5 such that the numbers made are divisible by 132​

To find: Two such numbers

Step-by-step explanation:

Solution:

132 = 2 * 2  * 3 * 11

=> 132 = 4 * 3 * 11

Divisible by 2 so the last digit should be even 2 or 4

a number is divisible by 4  if the sum of   two digits is divisible by 4

last two possible digits are

12, 52  ,  24

1 + 2 + 4 + 5 = 12  sum is divisible by 3    

So now remaining divisibility by 11

Subtract the last digit from a number made by the other digits. If that number is divisible by 11 then the original number is, too.

Ending with 12

5412       &  4512

541 - 12 = 539   then 53 - 9 = 44 divisible by 11

5412 is   divisible by 132

5412/132 =  41

4512  

451 - 2 = 449   then 44 - 9 = 35 not divisible by 11

Ending with 52

1452    & 4152

145 - 2 =  143     then 14 - 3 = 11   divisible by 11

1452 is  divisible by 132

1452/132 = 11

4152

415 - 2 = 413   then 41 - 3 = 38  not divisible by 11

Ending with

1524   & 5124

152 - 4 = 148    then 14 - 8 = 6  , not divisible by 11

5124

512 - 4 =  508  then  50 - 8 = 42  not divisible by 11

1452 & 5412 are  two 4-digits numbers using each the digits 1,2,4 and 5 such that the numbers made are divisible by 132​