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Why are all even number digit palindromes divisible by 11?
First, by induction it is shown that 102n-1 ≡ -1 (mod 11) for all natural numbers n (that is, all odd powers of 10 are one less than a multiple of 11.) i) When n = 1, then we have 102(1)-1 = 10, which is certainly congruent to -1 (mod 11). ii) Assume 102n-1 ≡ -1 (mod 11). Then, 102(n+1)-1 = 102n+2-1 = 102×102n-1 102 ≡ 1 (mod 11) and 102n-1 ≡ -1 (mod 11), so their product, 102×102n-1, is congruent to 1×(-1) = -1 (mod 11). Now that it is established that 10, 1000, 100000, ... are congruent to -1 (mod 11), it is clear that 11, 1001, 100001, ... are divisible by 11. Therefore, all integer multiples of these numbers are also divisible by 11. A palindrome containing an even number of digits may always be written as a sum of multiples of such numbers. The general form of such a palindrome, where all the As are integers between 0 and 9 inclusive, is A0 100 + A1 101 + ... + An 10n + An 10n+1 + ... + A1 102n + A0 102n+1 which may be rewritten as A0 (100 + 102n+1) + A1 (101 + 102n) + ... + An (10n + 10n+1) and again as 100 A0 (1 + 102n+1) + 101 A1 (1 + 102n-1) + ... + 10n An (1 + 101) Each of the factors in parentheses is one more than an odd power of 10, and is hence divisible by 11. Therefore, each term, the product of one such factor with two integers, is divisible by 11. Finally, the sum of terms divisible by 11 is itself divisible by 11. QED
How do you factor 11 plus 11 plus 88 equals?
11 + 11 + 88 = 11*(1 + 1 + 8) = 11*(10) = 110
Is the number 999977 a prime number?
No. It is divisible by 11.No. It is divisible by 11.No. It is divisible by 11.No. It is divisible by 11.
Is 123 divisible by 11?
No, it is not, but 121 and 132 are divisible by 11.
Is 11 divisible?
Yes. 11 is divisible by 1 and itself.
Is 6743021 divisible by 11?
No. 6,743,021 is not evenly divisible by 11.
Is 1793 divisible by 11?
Yes. 1,793 is evenly divisible by 11.
Why is 33 divisible by 3?
yes and if you ever want to know if something is divisible by 3 add up the number like 3 plus 3 (33) is 6 and it is divisible by 3. by the way the answer is 11. 11x3=33
Is 11 divisible by 8 and 3?
11 is divisible by no whole numbers except 1 and 11.
Are all palindromic numbers divisible by 11?
No. For instance, 101 is not divisible by 11.
Divisibility rule of 11?
if the difference of the sum at the alternate places is divisible by 11 then it is divisible by 11
How do you find out a number is divisible by 11?
Divide it by 11. If the answer is a whole number, it's divisible.
