Features that can be divisible by 2, 3, 4, 5, 6, 7, 8, and 9

Property 1: If numbers a and B can be divisible by c, their sum (a + B) or difference (a-B) can also be divisible by c.

Property 2: multiply several numbers. If one of the factors can be divisible by a certain number, their product can also be divisible by this number.

Number of divisible by 2,Number of digits in one digitCan be divisible by 2 (even numbers can be divisible by 2), then this number can be divisible by 2

Number of divisible by three,Numbers andIt can be divided by 3, so this number can be divided by 3

Number of divisible by four,Two digits of a single digit and ten digitsCan be divisible by four, so this number can be divisible by four

Number of divisible by 5,Number of digits with a single digit of 0 or 5Can be divided by 5, so this number can be divided by 5

Number of divisible by six,Numbers andDivisible by 3EvenIf a number can be divided by two and three, the number can be divided by six.

Number of divisible by 7,If a single digit of an integer is truncated, and then two times of the single digit is subtracted from the remaining number, if the difference is a multiple of 7, The original number can be divisible by 7. If the difference is too big or it is difficult to see whether it is a multiple of 7, we need to continue the process of "tail truncation, doubling, subtraction, and verification" until we can clearly determine whether it is possible. 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 example, the process of judging whether 6139 is a multiple of 7 is as follows: 613-9 × 2 = 595, 59-5 × 2 = 49, so 6139 is a multiple of 7, and so on.

Number of divisible by 8If the last three digits of an integer can be divisible by 8, the number must be divisible by 8.

Number of divisible by 9,Numbers and9 divisible, so this number can be 9 divisible

Number of divisible by 10,If a number can be divided by two and five, Then this number can be divisible by 10 (that is, the single digit is zero)

Number of divisible by 11,Odd digit(From left to right)Numbers andAnd the sum of numbers on the even bitsDifferenceIf the number is divisible by 11, the number can be divisible by 11. The multiple checksum of 11 can also be handled by the checksum of 7 above! The only difference in the process is that the multiples are not 2 but 1!
Number of integers that can be divisible by 12. If an integer can be divisible by 3 and 4, this number can be divisible by 12.

Number that can be divisible by 13. If a single digit of an integer is truncated, and then four times of the single digit is added from the remaining number, if the difference is a multiple of 13, then the original number can be divisible by 13. If the difference is too big or it is difficult to see whether it is a multiple of 13, we need to continue the process of "tail truncation, doubling, adding, and verification" until we can clearly determine whether it is possible.

Number that can be divisible by 17. If a single digit of an integer is truncated, and then five times of the single digit is subtracted from the remaining number, if the difference is a multiple of 17, then the original number can be divisible by 17. If the difference is too big or it is difficult to see whether it is a multiple of 17, we need to continue the process of "tail truncation, doubling, subtraction, and verification" until we can clearly determine whether it is possible.

Another method: if the difference between the last three digits of an integer and the first three digits of an integer can be divisible by 17, then the number can be divisible by 17.

Number that can be divisible by 19. If a single digit of an integer is truncated, and then two times of the single digit is added from the remaining number, if the difference is a multiple of 19, then the original number can be divisible by 19. If the difference is too big or it is difficult to see whether it is a multiple of 19, we need to continue the process of "tail truncation, doubling, adding, and verification" until we can clearly determine whether it is possible.

Another method: if the difference between the last three digits of an integer and the first seven times can be divisible by 19, the number can be divisible by 19.

Number of integers divisible by 23. If the difference between the last four digits of an integer and the first five times can be divisible by 23 (or 29), the number can be divisible by 23.

The number that can be divided by 25, and the two digits composed of ten digits and one digit can be divided by 25.

The Hundreds, ten, and single digits can be divisible by 125.

Features that can be divisible by 2, 3, 4, 5, 6, 7, 8, and 9