The divisibility of a number needs to judge the result according to the remainder of the dividend divided by the divisor, which requires memorizing the common characteristics of the divisibility of numbers. Remember more, contact more, and it will be OK.
Judging the number of digits of a number: 2 and 5, the number of digits of a number can be divisible by 2, which means that the number of digits of a number can be divisible by 2, and the number of digits of a number can be divisible by 5.
Judging the last two digits of a number: 4 and 25, the fact that the last two digits of a number can be divisible by 4 means that the whole number can be divisible by 4 and the fact that the last two digits of a number can be divisible by 25 means that the whole number can be divisible by 25;
Judge the last three digits of the number: 8 and 125, which can be divisible by 8, that is, the whole number can be divisible by 8, and the last three digits of the same number can be divisible by 125;
Judging the sum of digits of a number: 3 and 9, whether the sum of digits of a number is divisible by 3 means whether the integer of this number is divisible by 3. Similarly, whether the sum of digits of a number is divisible by 9 means whether the integer of this number is divisible by 9.
Parity check is simple. Integer divisible by 2 is even, 0 is even, and vice versa. The characteristics of applying the knowledge of parity to addition, subtraction, multiplication and division. Remember the commonly used features, and know that odd numbers often change the parity features of the whole operation result.
The application of consistency can subvert the speed of solving problems, and the value of prime numbers can only be obtained through addition and subtraction, otherwise the possibility of multiplication and division should be considered. In addition, it should be noted that 1 is neither a prime number nor a composite number, and 2 is the only even number among all prime numbers. Memorizing prime numbers within 20 is also beneficial to solving problems, which are 2, 3, 5, 7, 1 1, 13, 17, 65448 respectively.
The application of remainder features is often used to obtain a set of remainder results by dividing the dividend by a set of divisors, and the corresponding divisor and remainder features can be uniformly expressed as "dividend", such as:
If a number is divisible by 5+3, 6+3 and 7+3, it can be expressed as 2 10N+3.
If a number is divisible by 5+3, 6+2, 7+ 1, then this number can be expressed as 2 10N+8.
If a number is divisible by 5, 3, 6, 4 and 7, 5, then this number can be expressed as 2 10N-2.
In a simple word, congruence adds remainder, congruence adds sum, congruence subtracts difference, and the period is the least common multiple.
The mantissa function is used for multiplication and high digit operation. According to the different characteristics of answer digits, mantissa judgment method can be used to choose the answer. The mathematical operation of this application is usually a spike effect.
The application effect of special values is similar to mantissa. Some complex algebraic operations often use special values to get answers quickly and accurately, and can also reach the realm of seconds kill.