Tests of Divisibility-Divisibility by 40

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 40 with examples. 

Divisibility Test of 40:

A given number can be said to be divisible by 40 if that number is divisible by both 5 and 8. 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 40. Let us look at some other important divisibility tests, which act as a base. It includes divisibility tests of 5 and 8. 

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, 300 and 495 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, 300 has the last digit zero, so it is divisible by 5. The remaining digits are multiplied by 2 (30 x 2 = 60). The result is the same as the quotient when 300 is divided by 5 (300/5 = 60).

If the last digit is five, the result can be found by multiplying the remaining digits by two and can add one. For example, 495 has its last digit as 5, so it is divisible by 5. The remaining digits are multiplied by 2 (49 x 2 = 98) and one is added (98 + 1= 99). The result is the same as the quotient when 495 is divided by 5 (495/5 = 99).

 Example:

The last digit is 0:

1. 300 (the given number).
2. 300 (the last number is checked, should be 0 or 5)
3. 300 (if the last number is 0, then digits before the unit’s place is taken)
4. 30 x 2= 60 (the number before the last digit is multiplied by 2 and it is the final result).

The last digit is 5:

1. 495 (the given number).
2. 495 (the last number is checked, should be 0 or 5)
3. 495 (if the last number is 5, then digits before the unit’s place is taken)
4. 49 x 2 = 98+1=99  (the number before the last digit is multiplied by 2 and one is added, it is the final result).

Divisibility test of 8: 

Divisibility of 8 can be tested by checking the divisibility of the last three digits of the number by 8. If the last three digits of any given number are divisible by 8, then the entire number is divisible by 8. The reason for this property is because 1000 is divisible by 8. Regardless of the numbers before the last digit, the whole number will be divisible if the last three digits are divisible by 8. 

An alternative method to check the divisibility of 8 is by dividing the number by 2 thrice. If the number is divisible all three times, the given number is divisible by 8. The final value obtained in this method is the result of the given number.

 Example:

1. 4984 ( the given number).
2. 4984 (take the last three digits and check the divisibility). 
3. 984/8 = 123 (to check if the number is divisible by 8)
4. 4984/8 = 623 (as the previously chosen number is divisible, the given number is divisible by 8).

Alternate Method:

1. 4984 (the given number).
2. 4984/2 = 2492 (to check the divisibility)
3. 2492/2 = 1246 
4. 1246/2 = 623 (all the three times the number was divisible by 2, so it is divisible by 8)

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

Divisibility by 40:

A given number is said to be divisible by 40 if that number is divisible by both 5 and 8. From basic observation, it can be said that to be divisible by 40 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 8. 

For example, 

         Check if 2520 is divisible by 40.

1. 2520 (the last digit is chosen to check the divisibility of 5, should be 0 or 5).
2. 2520 (as the previous condition is satisfied, the last three digits are taken to check the divisibility of 8).
3. 520/8 = 65 (the given number is divisible by 8).

Check if 1555 is divisible by 40.

1. 1555 (the last digit is chosen to check the divisibility of 5, should be 0 or 5).
2. 1555 (as the previous condition is satisfied, the last three digits are taken to check the divisibility of 8).
3. 555/8 is not divisible by 8.

          So the given number is not divisible 40.

Conclusion

For any number to be divisible by 40, it should be divisible by 5 and 8. Learning the divisibility test of every number helps in speeding up the calculations and saves a lot of time. It is necessary to learn the divisibility test rules of the first 20 real numbers. These laws are helpful when the given number is long, and do not want to try dividing every integer to check the divisibility.