Tests of Divisibility-Divisibility by 80

Introduction

The divisibility tests are a set of rules framed, to check if a number can divide with another number without leaving behind a remainder. Divisibility rules are important in case the given number is long, these rules can be applied to check the divisibility without dividing them. These are quite useful to determine the factors of a number easily without actual division. This article covers the divisibility tests of 80 with examples. 

Divisibility Test of 80:

A given number can be said to be divisible by 80 if that number is divisible by both 5 and 16. The divisibility test refers to the ability of a number to divide the given number without actually dividing it. A number is said to be divisible if it leaves no remainder behind. Before studying in deep about the divisibility test of 80. Let us look at some other important divisibility tests, which act as a base. It includes divisibility tests of 5 and 16. 

Divisibility test of 5:

The divisibility of 5 can be easily verified by checking the unit’s place of a number. A given number is said to be divisible by 5 if its last digit is either zero or five. For example, 400 and 395 both ends with 0 or 5, hence both the numbers are divisible by 5. 

If the last digit is zero, the result can be found by multiplying the remaining digits by two. For example, 400 has the last digit is zero, so it is divisible by 5. The remaining digits are multiplied by 2 (40 x 2 = 80). The result is the same as the quotient when 400 is divided by 5 (400/5 = 80).

If the last digit is five, the result can be found by multiplying the remaining digits by two and can add one. For example, 395 has its last digit as 5, so it is divisible by 5. The remaining digits are multiplied by 2 (39 x 2 = 78) and one is added (78 + 1= 79). The result is the same as the quotient when 395 is divided by 5 (395/5 = 79).

Example:

The last digit is 0:

1. 400 (the given number).
2. 400 (the last number is checked, should be 0 or 5)
3. 400 (if the last number is 0, then digits before the unit’s place is taken)
4. 40 x 2= 80 (the number before the last digit is multiplied by 2 and it is the final result).

The last digit is 5:

1. 395 (the given number).
2. 395 (the last number is checked, should be 0 or 5)
3. 395 (if the last number is 5, then digits before the unit’s place is taken)
4. 39 x 2 = 78+1=79  (the number before the last digit is multiplied by 2 and one is added, it is the final result).

Divisibility test of 16

Divisibility of 16 can be tested by checking the divisibility of the last four digits of the number by 16. If the last four digits of any given number are divisible by 16, then the entire number is divisible by 16. The reason for this property is because 10000 is divisible by 16. Regardless of the numbers before the last digit, the whole number will be divisible if the last four digits are divisible by 16. 

An alternative method to check the divisibility of 16 is by dividing the number by 2 for four times. If the number is divisible all four times, the given number is divisible by 16. The final value obtained in this method is the result of the given number. 

Example:

1. 19936 ( the given number).
2. 19936 (take the last four digits and check the divisibility). 
3. 9936/16 = 621 (to check if the number is divisible by 16)
4. 19936/16 = 1246 (like the previously chosen number is divisible, the given number is divisible by 16).

Alternate Method:

1. 19936 (the given number).
2. 19936/2 = 9968 (to check the divisibility)
3. 9968/2 = 4984
4. 4984/2 = 2492 
5. 2492/2 = 1246 (all the four times the number was divisible by 2, so it is divisible by 16)

        As you can see the result is the same in both the methods.

 Divisibility by 80:

A given number is said to be divisible by 80 if that number is divisible by both 5 and 16. From basic observation, it can be said that to be divisible by 80 the given number should end with zero and cannot be odd. Apart from the observation, the given number should ultimately be divisible by both 5 and 16. 

 For example, 

         Check if 10080 is divisible by 80.

1. 10080 (the last digit is chosen to check the divisibility of 5, should be 0 or 5).
2. 10080 (as the previous condition is satisfied, the last four digits are taken to check the divisibility of 16).
3. 0080/16 = 5 (the given number is divisible by 16).

 Check if 2555 is divisible by 16.

1. 2555 (the last digit is chosen to check the divisibility of 5, should be 0 or 5).
2. 2555 (as the previous condition is satisfied, the last four digits are taken to check the divisibility of 16).
3. 555/8 is not divisible by 16.

          So the given number is not divisible 80.