Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 128)
128.
What is the unit digit in 7105 ?
Answer: Option
Explanation:
Unit digit in 7105 = Unit digit in [ (74)26 x 7 ]
But, unit digit in (74)26 = 1
Unit digit in 7105 = (1 x 7) = 7
Discussion:
17 comments Page 1 of 2.
Akshatha said:
2 decades ago
please tell me how to know that unit digit in 7 power 4 whole power 26 is 1..?
Aswath said:
2 decades ago
same doubt as akshatha hav!!!
Roja said:
2 decades ago
if we calculate 7 power 4, we will get unit digit is 1. so 1(unit digit) power anything is there, we will get 1 in unit digit
Sravanthi said:
1 decade ago
What is unit digit?
Bhagyasri said:
1 decade ago
How to know that unit digit of 7 power 4 whole to the power 26 is 1?
Keerthi said:
1 decade ago
Unit digit means which is in units place.
Rinky said:
1 decade ago
If we take nth power of a no having unit digit 1 then a no is obtained having unit digit 1. As unit digit of 7 power 4 is 1 so 26th power of a number having unit digit 1 is 1. i.e. (7^4)^26=a no having unit digit 1.
Prashanth said:
9 years ago
Why we are taking 7 power 4?
My doubt is why we are not taking another number like 7 power 3?
My doubt is why we are not taking another number like 7 power 3?
Pradeep said:
9 years ago
It's all about cyclicity.
Cyclicity: no of repetitions occurring in a multiple.
Exp :
7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = 117649.
So the cyclicity is 4 (no of patterns repeating).
So we must divide exponent by 4.
105/4 we get remainder 1.
Taking remainder 1 to cyclicity 7^1 = 7.
If the remainder is 2 then the answer is 7^2 = 9.
If the remainder is 3 then the answer is 7^3 = 3, and so on.
Cyclicity: no of repetitions occurring in a multiple.
Exp :
7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = 117649.
So the cyclicity is 4 (no of patterns repeating).
So we must divide exponent by 4.
105/4 we get remainder 1.
Taking remainder 1 to cyclicity 7^1 = 7.
If the remainder is 2 then the answer is 7^2 = 9.
If the remainder is 3 then the answer is 7^3 = 3, and so on.
(1)
Shadab said:
9 years ago
I don't understand cyclicity.
Why can't we do 7^2^(52) * 7?
By this way we get unit digit 3.
Why can't we do 7^2^(52) * 7?
By this way we get unit digit 3.
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