It works differently for each number. For 2, the last number has to be divisible by 2. For 3, the sum of the digits has to be divisible by 3 For 5, the number has to end with a 0 or a 5. For 7, it is kinda tricky. Take the last digit, double it, and subtract it from the numbers on the left. If the remainder is 0 or divisible by 7, the whole number is divisible by 7. For example 49: 9×2=18, 4-18=-14, -14/7=2 with remainder 0. For 700, 0×2=0, 70-0=70, 70/7=10 remainder 0.
This is usually specified for prime numbers, for non-prime number, you just do calculate the prime components of a number and combine the rules.
For example, divisibility by 15: it has to be divisible by 3 and 5. 1+5=6, 6/3=2 remainder 0. 15 ends with a 5. For number where with multiple same prime components the rules for these duplicate numbers have to apply multiple times. Like for 25, it has to end with a 5 or 0, and when dividing the number by 5, the result has to end with a 5 or a 0 aswell.