Characteristics of numbers divisible by 2:
If a number is divisible by 2, then the number at the end of the number is an even number, "0", "2", "4", "6", "8".
Characteristics of numbers divisible by 3:
If a number is divisible by 3, then the sum of all digits in the number is a multiple of 3. For example: 225 is divisible by 3, because 2 2 5=9, 9 is a multiple of 3, so 225 is divisible by 3.
Characteristics of numbers divisible by 4:
If the last two digits of a number are divisible by 4, the number is divisible by 4. For example: Can 15692512 be divisible by 4? Because the last two digits of 12 in 15692512 are divisible by 4, so 15692512 is divisible by 4.
Characteristics of numbers divisible by 5:
If a number ends in 0 or 5, then the number is divisible by 5.
Characteristics of numbers that are divisible by 7:
Method 1: If the one digit of an integer is truncated, then subtract 2 times the one digit from the remaining number. If the difference is a multiple of 7, the original number can be divided by 7. 7 is divisible. If the difference is too large or it is difficult to see if it is a multiple of 7 by mental arithmetic, it is necessary to continue the above process of "truncating, multiplying, subtracting, and checking the difference" until a clear judgment can be made. For example, the process of judging whether 133 is a multiple of 7 is as follows: 13-3×2=7, so 133 is a multiple of 7; for another example, the process of judging whether 6139 is a multiple of 7 is as follows: 613-9×2=595, 59- 5 x 2 = 49, so 6139 is a multiple of 7, and so on.
Method 2: If the difference between the last three digits of a multi-digit number and the number formed by the digits before the last three digits is a multiple of 7, then the number can be divisible by 7. For example: the last three digits of 280678 are 678, and the number formed by the last three digits is 280,679-280=399,399 which is divisible by 7, so 280679 is also divisible by 7.
Method 3: The first reduction method, reducing the multiple of 7.
For example, to determine whether 452669 is divisible by 7, 452669-420000=32669, as long as 32669 is divisible by 7. Continuing with 32669, 32669-28000=4669,4669-4200=469,469-420=49,49 is of course divisible by 7, so 452669 is divisible by 7.
Characteristics of numbers divisible by 8:
If the last three digits of an integer are divisible by 8, then the number is divisible by 8.
Characteristics of numbers divisible by 9:
If the sum of the digits in the digits of a number is divisible by 9, then the integer is divisible by 9. For example: Can 111111111 be divisible by 9? Because 1 1 1 1 1 1 1 1 1=9, 9 is a multiple of 9, so 111111111 is divisible by 9.
Characteristics of numbers divisible by 11:
Method 1: If the difference between the sum of odd digits and the sum of even digits (counting from right to left) of an integer is divisible by 11, then the number is divisible by 11. For example, to determine whether 491678 is divisible by 11. The sum of odd digits is 8 6 9=23; the sum of even 2 digits is 7 1 4=12; 23-12=11, 11 is divisible by 11, so 491678 is divisible by 11. This method is called "parity bit difference method".
Method 2: The multiple test method of 11 can also be handled by the "cut tail method" of the above-mentioned check 7! The only difference in the process is: the multiple is not 2 but 1! For example: to judge whether 491678 is divisible by 11, 49167-8=49159, 4915-9=4906, 490-6=484, 48-4=44. 44 is divisible by 11, so 491678 is divisible by 11.
Method 3: You can also judge according to method 2 of 7. For example: the last three digits of 283679 are 679, and the number formed by the last three digits is 283,679-283=396,396, which is divisible by 11, so 283679 must be divisible by 11.
Characteristics of numbers that are divisible by 13:
Method 1: If the one digit of an integer is truncated, and then add 4 times the one digit from the remaining number. If the sum is a multiple of 13, the original number can be divided by 13. Divisible by 13. If the sum is too large or it is difficult to see if it is a multiple of 13 by mental arithmetic, it is necessary to continue the above process of "truncating, multiplying, adding, and checking the sum" until a clear judgment can be made. For example, to determine whether 1284322 is divisible by 13. 128432 2×4=128440,12844 0×4=12844, 1284×4=1300,1300÷13=100. So 1284322 is divisible by 13.
Method 2: Method 2 of the previous 7 also applies to judgment 13.
For example: to determine whether 1284322 is divisible by 13, the last three digits of 128432 are 322, and the number formed by the digits before the end is 1284, 322-1284=-962. 962÷13=74. So 1284322 is divisible by 13.
Characteristics of numbers divisible by 17.
Method 1: If the one digit of an integer is truncated, and then subtract 5 times the one digit from the remaining number. If the difference is a multiple of 17, the original number is divisible by 17. If the difference is too large or it is difficult to see if it is a multiple of 17 by mental arithmetic, it is necessary to continue the above process of "truncating, multiplying, subtracting, and checking the difference" until a clear judgment can be made. For example, to determine whether 1675282 is divisible by 17, 167528-2×5=167518, 16751-8×5=16711, 1671-1×5=1666, 166-6×5=136, 136÷17=8, so 1675282 Divisible by 17.
Method 2: If the difference between the last three digits of an integer and the number that is separated by 3 times is divisible by 17, then the number is divisible by 17. For example, to judge whether 1675282 is divisible by 17, the last three digits of 1675282 are 282, the preceding number is 1675, 282-1675×3=-4743,4743÷17=279, so 1675282 is divisible by 17.
Characteristics of numbers that are divisible by 19:
Method 1: If the difference between the last three digits of an integer and the number that is separated by 7 times is divisible by 19, then the number is divisible by 19. For example, to determine whether 234555 is divisible by 19, the last three digits of 234555 are 555, and the first three digits are 234, 555-234×7=-1083, 1083÷19=57, so 234555 is divisible by 19.
Method 2: If the single digit of an integer is truncated, and then add 2 times the single digit from the remaining number. If the sum is a multiple of 19, the original number can be divisible by 19. If the sum is too large or it is difficult to see if it is a multiple of 19 by mental arithmetic, it is necessary to continue the above process of "truncating, multiplying, adding, and checking the sum" until a clear judgment can be made.
Characteristics of numbers divisible by 23:
If the difference between the last four digits of an integer and the number separated by 5 times before can be divisible by 23 (or 29), then the number is divisible by 23.
Characteristics of numbers divisible by 25:
If the last two digits of a number are divisible by 25, the number is divisible by 25.
Characteristics of numbers divisible by 125:
If the last three digits of a number are divisible by 125, then the number is divisible by 125.