Final answer:
Divisibility by 4 depends on the last two digits of a number being divisible by 4. Divisibility by 25 requires that the last two digits be 00, 25, 50, or 75. Both rules can be confirmed through experimentation and apply universally to all numbers.
Step-by-step explanation:
Divisibility Rules for 4 and 25
To determine whether a number is divisible by 4, you must look at the last two digits of the number. If the last two digits form a number that is divisible by 4, then the entire number is divisible by 4. This is because 100 (and multiples thereof) are always divisible by 4, so only the last two digits affect the divisibility by 4. An example is the number 312; since 12 is divisible by 4, the whole number 312 is divisible by 4.
For divisibility by 25, it's a similar concept but with a different focus. If the last two digits of a number are 00, 25, 50, or 75, the number is divisible by 25. This rule works because 100 is divisible by 25, and so any full hundreds plus an additional 0, 25, 50, or 75 would also be divisible. An example is the number 1350; since 50 is divisible by 25, the whole number 1350 is divisible by 25.
A way to test these rules is to use known cases and apply them to verify accuracy. The universality of mathematics ensures that these divisibility rules are applicable regardless of the context or situation, and they can be confirmed through experimentation and application to different cases. This approach to math allows students to understand the logic behind the rules and gain confidence in applying them.