Find the unit's digit in the product (2467)to the power 153 multiplied by (341)to the power 72?

Question

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Answer 1

All you have to worry about is the last digit of each number. This would be equivalent to:

7^153 * 1^72

The last part will be 1 (1 to any power is 1), so this reduces to, what is the last digit of 7^153?

Let's look at some of the results:
7^0 = 1
7^1 = 7
7^2 = (4)9
7^3 = (34)3
7^4 = (240)1
7^5 = (1680)7
...
See a pattern in the last digit? 1,7,9,3, 1,7,9,3,...The last digit will be the same for every 4 powers. In other words, if you take 153/4 (remainder 1), that means 7^153 will be the same as 7^1.

Hence the last digit will be 7.

Answer 2

You have asked for unit's place digit in

(2467^153)*(341^72)
At first I want to explain some rules:-
1) The unit place of the powered no. will be decided by unit place digit of base no.
Now first value in product is 2467 which has 7 at unit place so what ever be the power of 2467, 7 will decide the unit digit of the powered no.
2) For any given no., unit digit keep repeating after fix no. of time. For ex.
2^1=02(Unit place digit only)
2^2=04
2^3=08
2^4=16
2^5=32
In case of 2, unit digit repeats every 6Th time as it has cycle of 5.
Similarly, for 7, this cycles is of 4. So every fifth time digit at unit place will repeat.
Now power of 2467 is 153.
Here only 7 as a base is important as it is unit place digit in base no. so effectively we have to find the unit place digit in
7^153. As cycle for 7 is of 4 therefor
153%4=1 which gives us 7^1=7 at unit place.
So unit place digit in end result of
2467^153=7(unit place digit only) (i)
Similarly for 341^72
Here we actually have to find out unit place digit in
1^72=1(Unit place digit only) (ii)
Now on the basis of (i) and (ii)
We have
7*1=7(at unit place)
therefore
(2467^153) *(341^72)=7(unit's place digit)

Answer 3

Its 7
341 raised to power anything has last digit 1
2467 has 7 in the end which means 2467 power 4 will have last digit 1 in the end.
153 divided by 4 leaves remainder 1 so the last digit will be 7.

Answer 4

(2467)^153
Here 2467 is base and 153 is index
to find unit digit always divide index by 4 and find remainder,
153/ 4 = 38 integer and remainder is 1
so unit digit = 7^1-------- (7 is unit digit of 2467)
= 7
similarly (341)^72
72/4 remainder = 0
then unit digit = (1)^4 ------- (1 is unit digit of 341)
= 1
Product of 7 and 1 = 7
so unit digit in answer = 7

Answer 5

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Answer 6

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