Divisibility Test - Numbers

Category: Arithmetic

"Published in Newark, California, USA"

Perform the divisibility test of a number by 1 to 15 for 

Solution:

Consider the given number above

Without using a calculator, we can perform the divisibility test by using divisibility rules.

Divisibility by 1:

All numbers are divisible by 1 because 1 is a universal factor. Any number divided by 1 is always the same number.

Divisibility by 2:

Since the given number is an even number, then it is divisible by 2. All even numbers are divisible by 2.

Divisibility by 3:

To test a given number, add all the digits of a given number as follows

   
Since 9 is a multiple of 3, then the given number is divisible by 3.

Divisibility by 4:

Consider the given number 

Since 80 which is the last two digits of a given number is a multiple of 4, then the given number is divisible by 4.

Divisibility by 5:

Since the last digit of a given number is 0, then the given number is divisible by 5. A number that ends with 5 or 0 is divisible by 5. 

Divisibility by 6:

Since the given number is both divisible by 2 and 3, then it is divisible by 6.

Divisibility by 7:

To test a given number, double the last digit and then subtract it to the rest of the digits as follows
 

 

 

   
You can repeat the process as follows
 

 

 

Since -6 is not a multiple of 7, then the given number is not divisible by 7.

Divisibility by 8:

Consider the given number

Since 080 which is the last three digits of a given number is a multiple of 8, then the given number is divisible by 8.

Divisibility by 9:

To test a given number, add all the digits of a given number as follows 

Since 9 is a multiple of 9, then the given number is divisible by 9.

Divisibility by 10:

Since the last digit of a given number ends with 0, then the given number is divisible by 10. A number that ends with 0 is divisible by 10. 

Divisibility by 11:

To test a given number, create two groups of the sum of alternating digits and then get their difference as follows

Since 9 is not a multiple of 11, then the given number is not divisible by 11.

Divisibility by 12:

Since the given number is both divisible by 3 and 4, then it is divisible by 12. 

Divisibility by 13:

To test a given number, multiply the last digit by 4 and then add it to the rest of the digits as follows 

   

You can repeat the process as follows

  

Since 42 is not a multiple of 13, then the given number is not divisible by 13. 

Divisibility by 14:

Although the given number is an even number but it is not divisible by 7. Because of this, the given number is not divisible by 14.

Divisibility by 15:

Since the given number is both divisible by 3 and 5, then it is divisible by 15. 

Therefore,

1080 is divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, and 15.

Divisibility - 15

Category: Arithmetic

"Published in Newark, California, USA"

Divisibility by 15:

How do you know that a number is divisible by 15? Well, a number is divisible by 15 if it is both divisible by 3 and 5. In short, a number that ends with 5 or 0 that are divisible by 3.

Example 1:

The first thing that we need to do is to inspect the given number if it is divisible by 15 or not.

Since the last digit of a given number is not 5 or 0, then the given number is not divisible by 15. Any number multiply by another number that ends with 5 is always equal to a number that ends with 5 or 0. There's a remainder of 4 in the division. The answer or a quotient must be a whole number itself. You should not have a fraction or a remainder in the final answer.  

Example 2:

The first thing that we need to do is to inspect the given number if it is divisible by 15 or not.

Since the last digit of a given number is 5, then the given number is divisible by 5. 

Next, inspect the given number if it is divisible by 3 or not as  follows

Since 7 is not a multiple of 3, then the given number is not divisible by 3. Because of this, the given number is not divisible by 15. There's a remainder of 10 in the division. The answer or a quotient must be a whole number itself. You should not have a fraction or a remainder in the final answer. 

Example 3:

The first thing that we need to do is to inspect the given number if it is divisible by 15 or not.

Since the last digit of a given number is 0, then the given number is divisible by 5. 

Next, inspect the given number if it is divisible by 3 or not as  follows

Since 6 is a multiple of 3, then the given number is divisible by 3. Because of this, the given number is divisible by 15. There's no remainder or a fraction in the division.

You should consider in studying the divisibility of a number because you will use these principles later when you will study higher Math subjects that involves the division of a number, simplifying fractions, and even factoring. 

This method can also be used for negative integers as long as the given number is both divisible by 3 and 5. Again, there should be no remainder or a fraction in the division.