SOLUTION: What is the one�s digit of the number 7^2005?

Question 265435: What is the one�s digit of the number 7^2005?
Answer by vksarvepalli(154) (Show Source): You can put this solution on YOUR website!
to get the unit's digit of 7^2005
first we need to observe the pattern of the powers of 7
7^1 = 7 units digit is 7
7^2 = 49 (7*7) units digit is 9
7^3 = 243 (9*7) units digit is 3
7^4 = ---1 (3*7) units digit is 1
7^5 = ---7 (1*7) units digit is 7
again the sequence repeats
the sequence is 7,9,3,1
now for 7^2005 the power 2005 can be written as (4*501)+1
so 501 cycles will be completed
that means 7^2004 will end in 1
and for 2005 again the sequence starts and the units digit will be 7
so the one�s digit of the number 7^2005 is 7. (Answer)
RELATED QUESTIONS
What is the one�s digit of the number 7^2005... (answered by palanisamy,Theo,richwmiller)

What is the last digit of 2^2005 ? (a) 0 (b) 2 (c) 4 (d) 5 (e)... (answered by edjones)

the tens' digit of a two-digit number is one more than the units' digit. if the number is (answered by ankor@dixie-net.com)

What is the largest number which is the product of positive integers whose sum is... (answered by swincher4391)

The tens digit of a three digit number is three times the units digit and the units digit (answered by ankor@dixie-net.com)

The digits of a three-digit number add up to 18. If the ten�s digit is twice the... (answered by mananth)

What is the probability of a seven-digit (7) phone number containing the number seven... (answered by josmiceli)

I am thinking of a five-digit number where the fifth digit is one-half the fourth digit... (answered by Edwin McCravy,solver91311)

QUiZ TiME I am thinking of a five digit number, where the fifth digit is one-half the... (answered by Edwin McCravy)