Given that the number 1372x413 is divisible by 11, where x is a digit, then the value of x is
To find if number is divisible by 11, difference of sum of digits at even places and sum of digits at odd places should be either 0 or 11.
is this correct?????
Your rule is correct,
so the sum of the odd-place digits
= 1+7+x+1 = x+9
sum of even-place digits
= 3+2+4+3 = 12
difference :
x+9 - 12 = 0
x = 3
is 13723413 divisible by 11 ?
YES, 13723413 = 11(1247583)
Yes, that is correct! To determine if a number is divisible by 11, you can use the criterion you mentioned: the difference between the sum of the digits at even places and the sum of the digits at odd places should be either 0 or a multiple of 11.
In the case of the number 1372x413, let's assign the odd and even places as follows:
Odd places: 1, 7, x, 1, 3
Even places: 3, 2, 4
Now, we can calculate the sum of the digits at the odd and even places:
Sum of digits at odd places:
1 + 7 + x + 1 + 3 = 12 + x
Sum of digits at even places:
3 + 2 + 4 = 9
According to the divisibility rule for 11, the difference between the sum of the digits at odd places (12 + x) and the sum of the digits at even places (9) should be either 0 or a multiple of 11.
Therefore, we have the equation: (12 + x) - 9 = 3 + x = 0 or 11
To solve this equation, we can see that the only possible value for x is 8, as 3 + 8 = 11.
Hence, the value of x that makes 1372x413 divisible by 11 is 8.
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Thanks bye
almost. The sum must be divisible by 11.
Or, continue casting out 11's till you get to zero.
918082 is divisible by 11 (11*83462)
9-1+8-0+8-2 = 22
2-2 = 0