Number Divisibility Rules From 2 to 6
Hello. This math guide is on number divisibility rules for determining if a whole number can be divided by 2, 3, 4, 5 and 6.
Topics
- What Is The Point Of Divisibility Rules?
- Divisibility Rules For 2 to 6
- Practice Problems
- Answers To Practice Problems
What Is The Point Of Divisibility Rules?
One of the biggest and famous parts of mathematics is working with numbers. This includes addition, subtraction, multiplication and division. When it comes to divisibility rules, this falls under multiplying and division of numbers. (In a more general and technical sense this falls under the number theory branch of mathematics.)
Determining which (whole) numbers can be divided by other whole numbers helps with:
- Reducing And Simplifying Fractions To Lowest Terms
- Long Division
- Prime Factorization
- Determining Number Factors For Factoring Quadratic Equations
Divisibility Rules For 2 to 6
Divisibility rules for determining if a whole number can be divided by 2, 3, 4, 5 or 6 are not too difficult. With a good amount of practice, the student can easily memorize and understand the cases.
Which Numbers Are Even / Can Be Divided By Two?
Given a positive whole number greater than zero. A number that can be divded by two (even number) has a number in the ones place that is either a 2, 4, 6, 8 or 0. In other words, the whole number that is greater than 0 ends with a 2, 4, 6, 8 or 0.
Examples include 12, 20, 22, 48, 102, 222, 888, 138 and 3334.
Divisibility By Three
The divisibility rule by three is a useful one if the whole number is a large whole number. Given a whole number, the number is divisible by three if the digits of the number added together is a multiple of three.
For example, the number 111 is divisible by three as all the three ones add up to 3 which is a multiple of three.
A tougher example would involve something like the number 90210. Adding all the digits here gives 12 which is indeed a multiple of 3. We can conclude that the number 90210 can be divided by three.
Divisibility By Four
Finding out if a whole number is divisible by four involves one more extra step on the divisibility for 2. This extra step involves taking half again. That is, taking half of the half. If this half of the half is a whole number then the original (larger) number can be divided by four.
With the number 40, half of 40 is 20. Taking half again means taking half of 20 which gives 10. Because 10 is a whole number we can conclude that the original number 40 can be divided by 4.
Dividing by four is the same as taking a quarter of a number.
Divisibility By Five
If the whole number grater than 0 ends with a 5 or 0 then that whole number is divisible by five. Examples include 5, 10, 55, 1000, 1 million, 95 and 255.
Divisibility By Six
The rule for divisibility by six is quite simple. If the whole number is even (divisble by 2) and also divisible by three then that whole number is divisble by six.
Practice Problems
Is 332 an even number? Why?
Is 183 an odd number? Explain your answer.
Can the number 864 be divided by 6? Why?
List two numbers greater than 100 that are divisible by 5.
Can 100 be divided by four? Explain your answer.
Give an example of a number that is even but not divisible by 3.
Fill in the last digit by replacing the * such that the number would be divisible by 6. 18*
Answers To Practice Problems
The number 332 is an even number as it ends with a 2.
Yes, 183 is an odd number. The digits 1, 8 and 3 add up to 12 which is a multiple of 3.
The number 864 can be divided by 6. This number is even and adding the digits gives 18 which is a multiple of 3. This number is divisible by 2 and by 3 which makes 864 divisible by 6.
Answers vary. Easy choices include 105 and 110.
One hundred can be divided by four. Half of 100 is 50 and half of 50 is 25. Since 25 is a whole number this means that 100 can be divided by 4.
Give an example of a number that is even but not divisible by 3.
186
