Question

If 792 divides the integer 13xy45z, find the digits x,y, and z

Answer 1

Answer:

x= 8, y = 0, z = 6

Step-by-step explanation:

792 = 3^2 × 2^3 × 11.

therefore 13xy45z must be divisible by 9 , 8 and 11.

to make the number divisible by 9, we can have x+ y+z = 14 or 5.

Now 45z must be divisible by 8 to make the number divisible by 8.

thetefore, z= 6 (no other value is possible)

So x + y + z is 14(5 not possible since z is 6)

=> x + y = 8

now,

1+ x + 4 + 6(z) - 3-y-5 is divisible by 11

=> 3 + x - y is divisible by 11

=> x- y leaves remaining remainder 3 on division by 11

=> x-y = 8( 19 or greater is not possible because x,y are digits)

Clearly,

from the 2 equations obtained, x = 8, y = 0

pls mark my answer as brainliest. it required a lot of effort to type this question.