Divisibility - 13

Category: Arithmetic

"Published in Newark, California, USA

Divisibility by 13:

How do you know that a number is divisible by 13? Well, this method of checking and verifying a number is different or unique. You need to do this one. Multiply the last digit of a given number by 4 and then add it to the remaining digits. If the result is a multiple of 13, then the given number is divisible by 13. You can repeat the process if you wish until the result is a multiple of 13.

Example 1:

The first thing that we need to do is to inspect the given number if it is divisible by 13 or not. 

Multiply the last digit by 4 and then add it to the remaining digits as follows

Since 35 is not a multiple of 13, then the given number is not divisible by 13. There's a remainder of 3 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 13 or not. 

Multiply the last digit by 4 and then add it to the remaining digits as follows

Since 26 is a multiple of 13, then the given number is divisible by 13. 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 result of a process is a multiple of 13. Again, there should be no remainder or a fraction in the division.  
 

Divisibility - 12

Category: Arithmetic

"Published in Vacaville, California, USA"

Divisibility by 12:

How do you know that a number is divisible by 12? Well, a number is divisible by 12 if it is both divisible by 3 and 4.

Example 1:

The first thing that we need to do is to inspect the given number if it is divisible by 12 or not.

Since the given number is an odd number, then the given number is not divisible by 12. An even number multiply by an odd number or an even number is always an even number. There's a remainder of 9 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 12 or not.

Since the given number is an even number, then we can inspect the last two digits of a given number if it is divisible by 4 or not.

Since 50 is not a multiple of 4, then the given number is not divisible by 4. Because of this, the given number is not divisible by 12. There's a remainder of 6 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 12 or not.

Since the given number is an even number, then we can inspect the last two digits of a given number if it is divisible by 4 or not.
 
Since 68 is a multiple of 4, then the given number is divisible by 4. 

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

Since 2 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 12. There's a remainder of 8 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 4:

The first thing that we need to do is to inspect the given number if it is divisible by 12 or not.

Since the given number is an even number, then we can inspect the last two digits of a given number if it is divisible by 4 or not.
 
Since 72 is a multiple of 4, then the given number is divisible by 4. 

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

Since 9 is a multiple of 3, then the given number is divisible by 3. Because of this, the given number is divisible by 12. 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 4. Again, there should be no remainder or a fraction in the division.      

Divisibility - 11

Category: Arithmetic

"Published in Vacaville, California, USA"

Divisibility by 11:

How do you know that a number is divisible by 11? Well, a number is divisible by 11 if the difference of the two groups is a multiple of 11. Each group is the sum of the alternate digits of a given number. 

Example 1:

The first thing that we need to do is to inspect the given number if it is divisible by 11 or not.

The first group of alternating digits is 2, 7, and 6 and the second group of alternating digits is 0 and 3.

Hence, the difference of the two group is

 

Since the difference of the two groups is not a multiple of 11, then the given number is not divisible by 11. There's a remainder of 1 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 11 or not.

The first group of alternating digits is 8, 5, and 7 and the second group of alternating digits is 0, 3, and 6.

Hence, the difference of the two group is

Since the difference of the two groups is a multiple of 11, then the given number is divisible by 11. 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 difference of the two groups of the sum of alternating digits of a given number is a multiple of 11. Again, there should be no remainder or a fraction in the division.