Divisibility Rule of 5
Divisibility Rule of 5
Divisibility Rule of 5:
A number is divisible by 5, if its units digit is 0 or 5.
Justification:
Let n be any natural number. Then, n can be written as
n = 10a + b, where b is the units digit of n
Clearly, 10 is a multiple of 5. Therefore, 10a is also a multiple of 5.
The sum of any two multiples of 5 is a multiple of 5. Therefore, 10a+b will be a multiple of 5, if b is a multiple of 5.
Thus, an integer is divisible by 5, if its units digit is a multiple of 5. That is its units digit is either 0 or 5.
Hence the Test of Divisibility By 5 that is a number is divisible by 5, if its units digit is 0 or 5 is justified.
This implies that if the units digit of a number is not 0 or 5, then it is not divisible by 5.
In the general form since 10a is a multiple of 5. Therefore , when 10a + b is divided by 5, the remainder will be equal to the remainder when n is divided by 5.
Thus, the remainder when an integer is divided by 5 is equal to the remainder when its units digit is divided by 5.
Illustration : Write 521 in the form 10b + a then check its divisibility by 5
Solution: We will express 521 in the form 10b + a
where a = 1 and b = 52.
When 1 is divided by 5 it leaves a remainder as 1, So when 521 is divided by 5, the remainder is 1.
Check which of the following numbers are divisible by 5? 45678890, 24546677, 8798890, 4324535, 7989950, 6556773, 6778982, 643454, 2131342, 5678786 | |||
| Right Option : A | |||
| View Explanation | |||
Check which of the following numbers are not divisible by 5? 7837890, 2164672, 89270980, 8908770, 5264363, 67238765, 23564260,6754875 , 46467587, 78967643, 46587695, | |||
| Right Option : C | |||
| View Explanation | |||
Write 1348 in the form 10b + a then check its divisibility by 5. Find the value of a and b also. | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [20]
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