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A divisibility rule is a simple method for determining whether or not an integer is divisible by a fixed divisor without having to divide it by looking at its digits.
The three-digit divisibility rule asserts that if the sum of a whole number's digits is a multiple of three, the original number is also divisible by three.
The total of all the digits in 1377 is 1+3+7+7 = 18. Because 18 is divisible by three, 1377 is likewise divisible by three. The quotient is 1377 3 = 459, and the remainder is 0.
The divisibility rule of 9 asserts that if a number's sum of digits is divisible by 9, the number is divisible by 9 as well.
The three-digit divisibility rule and the nine-digit divisibility rule are quite similar. As previously stated, the divisibility rule for the divisibility test of 3 asserts that if a number's sum of all digits is divisible by 3, the number is also divisible by 3. The divisibility rule of 9 is similar to the divisibility rule of 3, in that a number is said to be divisible by 9 if the sum of all of its digits is divisible by 9.
Take 52884 for example. 52884 is divisible by three since the total of all digits is 5+2+8+8+4 = 27. The quotient is 52884 ÷ 3 = 17628, and the remainder is 0. It's worth noting that the sum of the digits is 27 is 2 + 7 = 9, which is likewise divisible by three.
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