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.    
 

Divisibility - 14

Category: Arithmetic

"Published in Newark, California, USA"

Divisibility by 14:

How do you know that a number is divisible by 14? Well, a number is divisible by 14 if it is both divisible by 2 and 7. In short, an even number that is divisible by 7. 

Example 1:

The first thing that we need to do is to inspect the given number if it is divisible by 14 or not.

Since the given number is an odd number, then the given number is not divisible by 14. An even number multiply by an odd number or an even number is always an even number. There's a remainder of 13 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 14 or not.

Since the given number is an even number, then we can inspect the given number if it is divisible by 7 or not as follows

Since 68 is not a multiple of 7, then the given number is not divisible by 7. Because of this, the given number is not divisible by 14. 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 14 or not.

Since the given number is an even number, then we can inspect the given number if it is divisible by 7 or not as follows

Since 28 is a multiple of 7, then the given number is divisible by 7. Because of this, the given number is divisible by 14. 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 2 and 7. Again, there should be no remainder or a fraction in the division.