The divisibility criteria help to determine whether or not a natural number is divisible by another natural number. We must remember what “to be divisible” means: we say that a natural number is divisible by another when, when we carry out this division, it has a null remainder, that is, when it is an exact division.
But imagine if to know if a number is or not divisible by another it was necessary to perform the division and check if the rest is null. This would become very tiring. Given this fact, the divisibility criteria help to determine which numbers are divisors of a given number.
Thus, we can say that the divisibility criteria are rules that allow determining the divisibility of numbers without the need to carry out long division processes.
Imagine yourself in the situation that Edson went through in the classroom:
"The teacher says to Edson: - Edson, you have 10 seconds to answer me if the number 1234567890 is divisible by the number 2".
Do you think Edson can do this division in less than 10 seconds? Is there any way for Edson to respond without having to split?
Edson will hardly be able to make this division in less than 10 seconds, however if he knows the divisibility criterion of number 2 he will be able to answer the teacher's question in less than 5 seconds.
For this, we will study the following divisibility criteria:
• Criteria for divisibility of the first 5 prime numbers:
• Divisibility by 2;
• Divisibility by 3;
• Divisibility by 5;
• Divisibility by 7;
• Divisibility by 11.
• Other divisibility criteria
• Divisibility by 4;
• Divisibility by 6;
• Divisibility by 8;
• Divisibility by 10.
By Gabriel Alessandro de Oliveira
Graduated in Mathematics
Take the opportunity to check out our video lesson on the subject: