1000 times 1000 is divisible by 2, 4, 5, 8 and 10.
I
Do the division, if there is no remainder, it is divisible. Seriously, many of the "divisibility rules" that have been discovered become more complicated than doing the actual division. For practical purposes, just learn the divisibility rules for a few simple cases (divisibility rules by 2, 4, 8, 5, 10, 3, 9, 7, 11, and 13), and for all other cases, just do the division.
The difference betweenthe sum of the digits in odd positions andthe sum of the digits in even positionsis divisible by 11.
928389 = 11 x 84399
90 with remainder 10.
I
It is: 1000/11 times 11 = 1000
Do the division, if there is no remainder, it is divisible. Seriously, many of the "divisibility rules" that have been discovered become more complicated than doing the actual division. For practical purposes, just learn the divisibility rules for a few simple cases (divisibility rules by 2, 4, 8, 5, 10, 3, 9, 7, 11, and 13), and for all other cases, just do the division.
The difference betweenthe sum of the digits in odd positions andthe sum of the digits in even positionsis divisible by 11.
The divisibility rule for 22 is that the number is divisible by 2 and by 11. Divisibility by 2 requires that the number ends in 0, 2, 4, 6 or 8. Divisibility by 11 requires that the difference between the sum of the the digits in odd positions and the sum of all the digits in even positions is 0 or divisible by 11.
if the difference of the sum at the alternate places is divisible by 11 then it is divisible by 11
1,100
Suppose you were trying to find the prime factorization of 123. You know that half of the divisors will be less than the square root. Since the square root is between 11 and 12, you only need to test 2, 3, 5, 7 and 11 as prime factors. If you know the rules of divisibility, you already know that 2 and 5 aren't factors and 3 is. It saves time.
928389 = 11 x 84399
The number must be divisible by 13 and by 11.
90 with remainder 10.
90 with remainder 10.