There can be instances where we have to find the unit digit of a number. Especially when exponent numbers of the form xy .To find the units digit of such numbers we need to only consider the units digits of the number x.
For example, if we need to find the units digit of a number like 567354, we need to consider only 7354. The units of 7354 will be the units digits of 567354. To find the units digit of xy when x is a single digit, such 2253,893,3774, etc., there are two cases:
That is, when x is any of the digits 2,4,6,or 8 and raised to powers which are multiple of 4 and when x is any of the digits 3,7, and 9 and raised to powers which are multiple of 4.
Qno.1: Find the units digit of 54357.
Answer: We can find the units digit of 54357 by finding the units digit of 357. We know that 57 gives a remainder of 1 when divided by 4.
57=14×4+1
So, the units digit of 357 is 1.
Hence, the units digit of 54357 = units digit of 357=1
Qno.2: Find the units digit of
.
Answer: can be written as
To find the units digit of, we need to find the units digits of 381. We know that 81 gives a remainder of 1 when divided by 4.
81=20×4+1
For numbers of the form xy and y=4q+r where r is the remainder when y is divided by 4, then, the units digit of xy is the units digit of xr.
Hence, units digit of=1
Qno.3: Find the units digit of
.
Answer: To find the remainder of
, we need to find the remainder of 
.
By the power rule in law of exponents, we know that
So, we can write as
So, to find the units digits of, we need to check the remainder of 72431
The remainder obtained when 2431 is divided by 4 is 3.
For numbers of the form xy and y=4q+r where r is the remainder when y is divided by 4, then, the units digit of xy is the units digit of xr.
So, units digit of 72431=3
Hence, the units digit of is 3.
For example, if we need to find the units digit of a number like 567354, we need to consider only 7354. The units of 7354 will be the units digits of 567354. To find the units digit of xy when x is a single digit, such 2253,893,3774, etc., there are two cases:
Case 1: When y in xy is NOT a multiple of 4
When y is NOT a multiple of 4, we need to find the remainder when y is divided by 4.Case 2: When y in xy is a multiple of 4
There are two conditions here, when x is an even number and when x is an Odd number.That is, when x is any of the digits 2,4,6,or 8 and raised to powers which are multiple of 4 and when x is any of the digits 3,7, and 9 and raised to powers which are multiple of 4.
Solved Examples
Qno.1: Find the units digit of 54357.
Answer: We can find the units digit of 54357 by finding the units digit of 357. We know that 57 gives a remainder of 1 when divided by 4.
57=14×4+1
So, the units digit of 357 is 1.
Hence, the units digit of 54357 = units digit of 357=1
Qno.2: Find the units digit of
.Answer:
can be written as To find the units digit of
, we need to find the units digits of 381. We know that 81 gives a remainder of 1 when divided by 4. 81=20×4+1
For numbers of the form xy and y=4q+r where r is the remainder when y is divided by 4, then, the units digit of xy is the units digit of xr.
Hence, units digit of
=1 Qno.3: Find the units digit of
.Answer: To find the remainder of
, we need to find the remainder of . By the power rule in law of exponents, we know that
So, we can write
as So, to find the units digits of
, we need to check the remainder of 72431 The remainder obtained when 2431 is divided by 4 is 3.
For numbers of the form xy and y=4q+r where r is the remainder when y is divided by 4, then, the units digit of xy is the units digit of xr.
So, units digit of 72431=3
Hence, the units digit of
is 3.