THE RULES OF DIVISIBILITY

As some of you may know, some numbers are divisible by many other numbers.

But finding what a number is divisible by can be quite difficult, if you don't have a calculator.

Today, we will learn a few simple rules on how to find what a number is divisible by.

How do you know if a number is divisible by two?

Numbers come in two different types, even or odd. All even numbers are divisible by two.

An easy way to find an even number is to see if the number ends in a 2, 4, 6, 8, or 0.

An example that follows this rule is the number 118. It ends in an 8 so it can be divided by 2.

The number 57 cannot follow this rule because it ends in an odd number.

How do you know if a number is divisible by three?

To find if a number is divisible by three, add all of the digits, and divide the sum by three.

To help you better understand, let's use the number 87.

In the number 87, you add 8 and 7 to get 15 and 15 divided by 3 is 5 so 87 is divisible by 3.

The number 118 is not divisible be 3 because 1+1+8=10 and 10 is not divisible by 3.

How do you find if a number is divisible by four?

To find if a number is divisible by four, you look at the last two digits and if they are divisible by four, so is the number as a whole.

A great example showing this is the number 736.

The number 736 ends in 36, and if you know your basic facts, you know that 4 times 9 is 36, making 736 divisible by 4.

An example that doesn't follow this rule is 42, which is not divisible by 4.

How do you find if a number is divisible by five?

This rule is one of the easiest to remember.

All you have to know is that if the number ends in a 5 or a 0 it is divisible by 5.

The number 270 ends in 0 so it is divisible by 5.

The number 53 ends in a 3, making 5 unable to go into it.

How do you know if a number is divisible by six?

All you you need to know for this are the rules for two and three.

It needs to be both an even number, and all of the digits combined must be divisible by three.

An example of this is the number 1,212, which is both even, and 1+1+2+2=6 which is divisible by 3, making 6 able to go into it.

A number that doesn't follow this rule is the number 3,579, which when added, equals 24 and is divisible by 3, but is not divisible by 2.

How do you know is a number is divisible by ten?

The rule for the number ten is much easier than the rule for five.

All you have to remember is that all numbers that end in a 0 are divisible by 10.

An example of a number divisible by 10 is the number 59,248,580 which ends in a 0, you might say 20 also works.

Some numbers that don't follow this rule are the numbers 53 and 3,141,592 because they don't end in a 0.

To test the knowledge you have learned during this presentation, we will take the number of feet in a mile, 5,280, and apply the rules that we have gone over.

WHICH OF THE FOLLOWING GO INTO THE NUMBER 5,280?

• 2
• 3
• 4
• 5
• 6
• 10
• All of the Above

Answer:

All of the above.
It is an even number, the sum of the digits is divisible by 3, the last two digits are divisible by 4, and it ends in a 0. This applies to all of the rules that we have gone over.

These rules will help you find factors for the larger numbers you may come across during a fraction unit.

If you have to simplify a fraction, knowing these rules will shorten the time spent on a math problem dramatically.

An example of how this would work is the fraction 4/10.

To simplify, you divide the top and bottom by 2 to get 2/5.

Knowing the factors and the rules will help you simplify any fraction you come across no matter how big the number may be.

Thank you for watching and I hope you learned how to conquer fractions using the rules of divisibility.